{"id":5001,"date":"2016-05-19T11:49:00","date_gmt":"2016-05-19T06:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-9-maths-exercise-9-4\/"},"modified":"2018-06-18T16:22:19","modified_gmt":"2018-06-18T10:52:19","slug":"ncert-solutions-for-class-9-maths-exercise-9-4","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-9-4\/","title":{"rendered":"NCERT Solutions for Class 9 Maths Exercise 9.4"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_76 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-9-4\/#NCERT_Solutions_for_Class_9_Mathematics_Areas_of_Parallelograms_and_Triangles\" >NCERT Solutions for Class 9 Mathematics\u00a0Areas of Parallelograms and Triangles<\/a><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-9-4\/#1_Parallelogram_ABCD_and_rectangle_ABEF_are_on_the_same_base_AB_and_have_equal_areas_Show_that_the_perimeter_of_the_parallelogram_is_greater_than_that_of_the_rectangle\" >1. Parallelogram ABCD and rectangle ABEF are on the same base AB and have equal areas. Show that the perimeter of the parallelogram is greater than that of the rectangle.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-9-4\/#2_In_figure_D_and_E_are_two_points_on_BC_such_that_BD_DE_EC_Show_that_ar_ABD_ar_ADE_ar_AEC_Can_you_know_answer_the_question_that_you_have_left_in_the_%E2%80%98introduction_of_this_chapter_whether_the_field_of_Budhia_has_been_actually_divided_into_three_parts_of_equal_area\" >2. In figure, D and E are two points on BC such that BD = DE = EC. Show that ar (ABD) = ar (ADE) = ar (AEC). Can you know answer the question that you have left in the \u2018introduction\u2019 of this chapter, whether the field of Budhia has been actually divided into three parts of equal area?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-9-4\/#3_In_figure_ABCD_DCFE_and_ABFE_are_parallelograms_Show_that_ar_ADE_ar_BCF\" >3. In figure, ABCD, DCFE and ABFE are parallelograms. Show that ar (ADE) = ar (BCF).<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-9-4\/#4_In_figure_ABCD_is_a_parallelogram_and_BC_is_produced_to_a_point_Q_such_that_AD_CQ_If_AQ_intersects_DC_at_P_show_that_ar_BPC_ar_DPQ\" >4. In figure, ABCD is a parallelogram and BC is produced to a point Q such that AD = CQ. If AQ intersects DC at P, show that ar (BPC) = ar (DPQ).<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-9-4\/#5_In_figure_ABC_and_BDF_are_two_equilateral_triangles_such_that_D_is_the_mid-point_of_BC_If_AE_intersects_BC_at_F_show_that\" >5. In figure, ABC and BDF are two equilateral triangles such that D is the mid-point of BC. If AE intersects BC at F, show that:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-9-4\/#6_Diagonals_AC_and_BD_of_a_quadrilateral_ABCD_intersect_each_other_at_P_Show_that\" >6. Diagonals AC and BD of a quadrilateral ABCD intersect each other at P. Show that:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-9-4\/#7_P_and_Q_are_respectively_the_mid-points_of_sides_AB_and_BC_or_a_triangle_ABC_and_R_is_the_mid-point_of_AP_show_that\" >7. P and Q are respectively the mid-points of sides AB and BC or a triangle ABC and R is the mid-point of AP, show that:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-9-4\/#8_In_figure_ABC_is_a_right_triangle_right_angled_at_A_BCED_ACFG_and_ABMN_are_squares_on_the_sides_BC_CA_and_AB_respectively_Line_segment_AXDE_meets_BC_at_Y_Show_that\" >8. In figure, ABC is a right triangle right angled at A. BCED, ACFG and ABMN are squares on the sides BC, CA and AB respectively. Line segment AXDE meets BC at Y. Show that:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-9-4\/#ii_From_above_MBC_ABD\" >(ii) From above, MBC ABD<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-9-4\/#iii_Join_AM_ABMN_is_a_square\" >(iii) Join AM. ABMN is a square.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-9-4\/#iv_In_FCB_and_ACE\" >(iv) In FCB and ACE,<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-9-4\/#v_From_iv_we_have_FCB_ACE\" >(v) From (iv), we have, FCB ACE<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-9-4\/#vi_Join_AF_ACFG_is_a_square\" >(vi) Join AF. ACFG is a square.<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-9-4\/#NCERT_Solutions_for_Class_9_Maths_Exercise_94\" >NCERT Solutions for Class 9 Maths Exercise 9.4<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-9-4\/#CBSE_app_for_Class_9\" >CBSE app for Class 9<\/a><\/li><\/ul><\/nav><\/div>\n<p>NCERT Solutions for Class 9 Maths Exercise 9.4 book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 9 Maths chapter wise NCERT solution for Maths Book for all the chapters can be downloaded from our website and myCBSEguide mobile app for free.<\/p>\n<p style=\"text-align: center;\"><strong>NCERT solutions for Class 9 Maths\u00a0<\/strong><strong>Areas of Parallelograms and Triangles<\/strong><strong>\u00a0<\/strong><strong><a class=\"button\" href=\"https:\/\/mycbseguide.com\/downloads\/cbse-class-09-mathematics-areas-of-parallelograms-and-triangles\/1243\/ncert-solutions\/5\/\">Download as PDF<\/a><\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/media-mycbseguide.s3.ap-south-1.amazonaws.com\/images\/blog\/09_Class_Maths_Book.jpg\" alt=\"NCERT Solutions for Class 9 Maths Exercise 9.4\" width=\"180\" height=\"232\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_9_Mathematics_Areas_of_Parallelograms_and_Triangles\"><\/span>NCERT Solutions for Class 9 Mathematics\u00a0Areas of Parallelograms and Triangles<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"1_Parallelogram_ABCD_and_rectangle_ABEF_are_on_the_same_base_AB_and_have_equal_areas_Show_that_the_perimeter_of_the_parallelogram_is_greater_than_that_of_the_rectangle\"><\/span><strong>1. Parallelogram ABCD and rectangle ABEF are on the same base AB and have equal areas. Show that the perimeter of the parallelogram is greater than that of the rectangle.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. Give<\/strong>n: Parallelogram ABCD and rectangle ABEF are on same base AB and between the same parallels AB and CF.<\/p>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 1594\" style=\"height: 124px; width: 215px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image001.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image002.png\" \/>ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image003.png\" \/>gm ABCD) = ar (rect. ABEF)<\/p>\n<p style=\"text-align: justify;\"><strong>To prove<\/strong>: AB + BC + CD + AD &gt; AB + BE + EF + AF<\/p>\n<p style=\"text-align: justify;\"><strong>Proof<\/strong>: AB = CD [<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image004.png\" \/> opposites sides of a parallelogram are always equal]\n<p style=\"text-align: justify;\">AB = EF [<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image004.png\" \/> opposites sides of a rectangle are always equal]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image002.png\" \/>CD = EF<\/p>\n<p style=\"text-align: justify;\">Adding AB both sides,<\/p>\n<p style=\"text-align: justify;\">AB + CD = AB + EF \u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image002.png\" \/>Off all the segments that can be drawn to a given line from a point not lying on it, the perpendicular segment is the shortest.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image002.png\" \/>BE &lt; BC and AF &lt; AD<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/>BC &gt; BE and AD &gt; AF<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image002.png\" \/>BC + AD &gt; BE + AF \u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\">From eq. (i) and (ii),<\/p>\n<p style=\"text-align: justify;\">AB + CD + BC + AD = AB + EF + BE + AF<\/p>\n<hr \/>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"2_In_figure_D_and_E_are_two_points_on_BC_such_that_BD_DE_EC_Show_that_ar_ABD_ar_ADE_ar_AEC_Can_you_know_answer_the_question_that_you_have_left_in_the_%E2%80%98introduction_of_this_chapter_whether_the_field_of_Budhia_has_been_actually_divided_into_three_parts_of_equal_area\"><\/span><strong>2. In figure, D and E are two points on BC such that BD = DE = EC. Show that ar (ABD) = ar (ADE) = ar (AEC). Can you know answer the question that you have left in the \u2018introduction\u2019 of this chapter, whether the field of Budhia has been actually divided into three parts of equal area? <\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 1597\" style=\"height: 129px; width: 166px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image006.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>In <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ABC, points D and E divides BC in three equal parts such that BD = DE = EC.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image002.png\" \/>BD = DE = EC = <img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image008.png\" \/> BC<\/p>\n<p style=\"text-align: justify;\">Draw AF<img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image009.png\" \/>BC<\/p>\n<p style=\"text-align: justify;\">ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ABC) = <img decoding=\"async\" style=\"height: 41px; width: 85px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image010.png\" \/> \u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\">and ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ABD) =<img decoding=\"async\" style=\"height: 42px; width: 85px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image011.png\" \/> \u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 84px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image012.png\" \/> = <img decoding=\"async\" style=\"height: 45px; width: 119px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image013.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image008.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ABC) \u2026\u2026\u2026.(iii)<\/p>\n<p style=\"text-align: justify;\">And ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>AEC) = <img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image008.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ABC) \u2026\u2026\u2026.(iv)<\/p>\n<p style=\"text-align: justify;\">From (ii), (iii) and (iv),<\/p>\n<p style=\"text-align: justify;\">ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ABD) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ADE) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>AEC)<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 9.4<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"3_In_figure_ABCD_DCFE_and_ABFE_are_parallelograms_Show_that_ar_ADE_ar_BCF\"><\/span><strong>3. In figure, ABCD, DCFE and ABFE are parallelograms. Show that ar (ADE) = ar (BCF). <\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 1600\" style=\"height: 132px; width: 204px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image014.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>As we know that opposite sides of a parallelogram are always equal.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image002.png\" \/>In parallelogram ABFE, AE = BF and AB = EF<\/p>\n<p style=\"text-align: justify;\">In parallelogram DCFE, DE = CF and DC = EF<\/p>\n<p style=\"text-align: justify;\">In parallelogram ABCD, AD = BC and AB = DC<\/p>\n<p style=\"text-align: justify;\">Now in <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ADE and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BCF,<\/p>\n<p style=\"text-align: justify;\">AE = BF [Opposite sides of parallelogram ABFE]\n<p style=\"text-align: justify;\">DE = CF [Opposite sides of parallelogram DCFE]\n<p style=\"text-align: justify;\">And AD = BC [Opposite sides of parallelogram ABCD]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image002.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ADE <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image015.png\" \/> <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BCF [By SSS congruency]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image002.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ADE) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BCF)<\/p>\n<p style=\"text-align: justify;\">[<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image004.png\" \/> Area of two congruent figures is always equal]\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 9.4<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"4_In_figure_ABCD_is_a_parallelogram_and_BC_is_produced_to_a_point_Q_such_that_AD_CQ_If_AQ_intersects_DC_at_P_show_that_ar_BPC_ar_DPQ\"><\/span><strong>4. In figure, ABCD is a parallelogram and BC is produced to a point Q such that AD = CQ. If AQ intersects DC at P, show that ar (BPC) = ar (DPQ). <\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 1603\" style=\"height: 183px; width: 156px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image016.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Join A and C.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>APC and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BPC are on the same base PC and between the same parallels PC and AB.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image002.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>APC) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BPC) \u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\">Now ACBD is a parallelogram.<\/p>\n<p style=\"text-align: justify;\">AD = BC [opposite sides of a parallelogram are always equal]\n<p style=\"text-align: justify;\">Also BC = CQ [given]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image002.png\" \/>AD = CQ<\/p>\n<p style=\"text-align: justify;\">Now AD <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image003.png\" \/> CQ [Since CQ is the extension of BC]\n<p style=\"text-align: justify;\">And AD = CQ<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image002.png\" \/>ADQC is a parallelogram.<\/p>\n<p style=\"text-align: justify;\">[<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image004.png\" \/> If one pair of opposite sides of a quadrilateral is equal and parallel then it is a parallelogram]\n<p style=\"text-align: justify;\">Since diagonals of a parallelogram bisect each other.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image002.png\" \/>AP = PQ and CP = DP<\/p>\n<p style=\"text-align: justify;\">Now in <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>APC and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>DPQ,<\/p>\n<p style=\"text-align: justify;\">AP = PQ [Proved above]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image017.png\" \/>APC = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image017.png\" \/>DPQ [Vertically opposite angles]\n<p style=\"text-align: justify;\">PC = PD [Prove above]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image002.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>APC <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image015.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>DPQ \u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>APC) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>DPQ) [area of congruent figures is always equal]\n<p style=\"text-align: justify;\">From eq. (i) and (ii),<\/p>\n<p style=\"text-align: justify;\">ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BPC) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>DPQ)<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 9.4<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"5_In_figure_ABC_and_BDF_are_two_equilateral_triangles_such_that_D_is_the_mid-point_of_BC_If_AE_intersects_BC_at_F_show_that\"><\/span><strong>5. In figure, ABC and BDF are two equilateral triangles such that D is the mid-point of BC. If AE intersects BC at F, show that:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 1606\" style=\"height: 204px; width: 161px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image018.jpg\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(i) ar (BDE) = <\/strong><img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image019.png\" \/><strong> ar (ABC)<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) ar (BDE) = <\/strong><img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/><strong> ar (BAE)<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) ar (ABC) = 2 ar (BEC)<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iv) ar (BFE) = ar (AFD)<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(v) ar (BFE) = 2 ar (FED)<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(vi) ar (FED) = <\/strong><img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image021.png\" \/><strong> ar (AFC)<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Join EC and AD.<\/p>\n<p style=\"text-align: justify;\">Since <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ABC is an equilateral triangle.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image002.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image017.png\" \/>A = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image017.png\" \/>B = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image017.png\" \/>C = <img decoding=\"async\" style=\"height: 21px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image022.png\" \/><\/p>\n<p style=\"text-align: justify;\">Also <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BDE is an equilateral triangle.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image002.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image017.png\" \/>B = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image017.png\" \/>D = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image017.png\" \/>E = <img decoding=\"async\" style=\"height: 21px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image022.png\" \/><\/p>\n<p style=\"text-align: justify;\">If we take two lines, AC and BE and BC as a transversal.<\/p>\n<p style=\"text-align: justify;\">Then <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image017.png\" \/>B = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image017.png\" \/>C = <img decoding=\"async\" style=\"height: 21px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image022.png\" \/>[Alternate angles]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/>BE <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image003.png\" \/> AC<\/p>\n<p style=\"text-align: justify;\">Similarly, for lines AB and DE and BF as transversal.<\/p>\n<p style=\"text-align: justify;\">Then <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image017.png\" \/>B = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image017.png\" \/>C = <img decoding=\"async\" style=\"height: 21px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image022.png\" \/>[Alternate angles]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/>BE <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image003.png\" \/> AC<\/p>\n<p style=\"text-align: justify;\"><strong>(i)<\/strong> Area of equilateral triangle BDE = <img decoding=\"async\" style=\"height: 45px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image023.png\" \/> (BD)<sup>2<\/sup> \u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\">Area of equilateral triangle ABC = <img decoding=\"async\" style=\"height: 45px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image023.png\" \/> (BC)<sup>2<\/sup> \u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\">Dividing eq. (i) by (ii),<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 85px; width: 160px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image024.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/><img decoding=\"async\" style=\"height: 85px; width: 169px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image025.png\" \/> [<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image004.png\" \/> BD = DC]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/><img decoding=\"async\" style=\"height: 56px; width: 144px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image026.png\" \/> <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/><img decoding=\"async\" style=\"height: 49px; width: 103px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image027.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BDE) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image019.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ABC)<\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> In <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BEC, ED is the median.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image002.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BEC) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BAE) \u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\">[Median divides the triangle in two triangles having equal area]\n<p style=\"text-align: justify;\">Now BE <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image003.png\" \/> AC<\/p>\n<p style=\"text-align: justify;\">And <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BEC and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BAE are on the same base BE and between the same parallels BE and AC.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image002.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BEC) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BAE) \u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\">Using eq. (i) and (ii), we get<\/p>\n<p style=\"text-align: justify;\">Ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BDE) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BAE)<\/p>\n<p style=\"text-align: justify;\"><strong>(iii)<\/strong> We have ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BDE) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image019.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ABC) [Proved in part (i)] \u2026\u2026\u2026.(iii)<\/p>\n<p style=\"text-align: justify;\">ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BDE) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image019.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BAE) [Proved in part (ii)]\n<p style=\"text-align: justify;\">ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BDE) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image019.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BEC) [Using eq. (iii)] \u2026\u2026\u2026.(iv)<\/p>\n<p style=\"text-align: justify;\">From eq. (iii) and (iv), we het<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image019.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ABC) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image019.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BEC)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ABC) = 2 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BEC)<\/p>\n<p style=\"text-align: justify;\"><strong>(iv)<\/strong> <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BDE and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>AED are on the same base DE and between same parallels AB and DE.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image002.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BDE) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>AED)<\/p>\n<p style=\"text-align: justify;\">Subtracting <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>FED from both the sides,<\/p>\n<p style=\"text-align: justify;\">ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BDE) \u2013 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>FED) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>AED) \u2013 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>FED)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BFE) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>AFD) \u2026\u2026\u2026.(v)<\/p>\n<p style=\"text-align: justify;\"><strong>(v)<\/strong> An in equilateral triangle, median drawn is also perpendicular to the side,<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image002.png\" \/>AD <img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image009.png\" \/> BC<\/p>\n<p style=\"text-align: justify;\">Now ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>AFD) = <img decoding=\"async\" style=\"height: 41px; width: 99px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image028.png\" \/> \u2026\u2026\u2026.(vi)<\/p>\n<p style=\"text-align: justify;\">Draw EG <img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image009.png\" \/> BC<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image002.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>FED) = <img decoding=\"async\" style=\"height: 41px; width: 99px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image029.png\" \/> \u2026\u2026\u2026.(vii)<\/p>\n<p style=\"text-align: justify;\">Dividing eq. (vi) by (vii), we get<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 80px; width: 160px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image030.png\" \/> <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/><img decoding=\"async\" style=\"height: 49px; width: 117px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image031.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/><img decoding=\"async\" style=\"height: 85px; width: 140px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image032.png\" \/> [Altitude of equilateral triangle = <img decoding=\"async\" style=\"height: 45px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image023.png\" \/> side]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/><img decoding=\"async\" style=\"height: 49px; width: 125px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image033.png\" \/> [D is the mid-point of BC]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/><img decoding=\"async\" style=\"height: 49px; width: 100px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image034.png\" \/> <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>AFD) = 2 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>FED) \u2026\u2026(viii)<\/p>\n<p style=\"text-align: justify;\">Using the value of eq. (viii) in eq. (v),<\/p>\n<p style=\"text-align: justify;\">Ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BFE) = 2 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>FED)<\/p>\n<p style=\"text-align: justify;\"><strong>(vi)<\/strong> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>AFC) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>AFD) + ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ADC) = 2 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>FED) + <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ABC) [using (v)<\/p>\n<p style=\"text-align: justify;\">= 2 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>FED) + <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> [4 <img decoding=\"async\" style=\"height: 14px; width: 12px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image035.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BDE)] [Using result of part (i)]\n<p style=\"text-align: justify;\">= 2 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>FED) + 2 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BDE) = 2 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>FED) + 2 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>AED)<\/p>\n<p style=\"text-align: justify;\">[<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BDE and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>AED are on the same base and between same parallels]\n<p style=\"text-align: justify;\">= 2 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>FED) + 2 [ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>AFD) + ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>FED)]\n<p style=\"text-align: justify;\">= 2 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>FED) + 2 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>AFD) + 2 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>FED) [Using (viii)]\n<p style=\"text-align: justify;\">= 4 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>FED) + 4 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>FED)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>AFC) = 8 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>FED)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>FED) = <img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image021.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>AFC)<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 9.4<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"6_Diagonals_AC_and_BD_of_a_quadrilateral_ABCD_intersect_each_other_at_P_Show_that\"><\/span><strong>6. Diagonals AC and BD of a quadrilateral ABCD intersect each other at P. Show that:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>ar (APB) <img decoding=\"async\" style=\"height: 14px; width: 12px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image035.png\" \/> ar (CPD) = ar (APD) <img decoding=\"async\" style=\"height: 14px; width: 12px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image035.png\" \/> ar (BPC)<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. Given<\/strong>: A quadrilateral ABCD, in which diagonals AC and BD intersect each other at point E.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 1609\" style=\"height: 140px; width: 193px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image036.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>To Prove<\/strong>: ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>AED) <img decoding=\"async\" style=\"height: 14px; width: 12px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image035.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BEC)<\/p>\n<p style=\"text-align: justify;\">= ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ABE) <img decoding=\"async\" style=\"height: 14px; width: 12px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image035.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>CDE)<\/p>\n<p style=\"text-align: justify;\"><strong>Construction<\/strong>: From A, draw AM <img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image009.png\" \/> BD and from C, draw CN <img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image009.png\" \/> BD.<\/p>\n<p style=\"text-align: justify;\"><strong>Proof<\/strong>: ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ABE) = <img decoding=\"async\" style=\"height: 41px; width: 88px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image037.png\" \/> \u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\">And ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>AED) = <img decoding=\"async\" style=\"height: 41px; width: 92px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image038.png\" \/> \u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\">Dividing eq. (ii) by (i), we get,<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 80px; width: 179px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image039.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/><img decoding=\"async\" style=\"height: 49px; width: 117px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image040.png\" \/> \u2026\u2026\u2026.(iii)<\/p>\n<p style=\"text-align: justify;\">Similarly <img decoding=\"async\" style=\"height: 49px; width: 117px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image041.png\" \/> \u2026\u2026\u2026.(iv)<\/p>\n<p style=\"text-align: justify;\">From eq. (iii) and (iv), we get<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 49px; width: 77px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image042.png\" \/> = <img decoding=\"async\" style=\"height: 49px; width: 77px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image043.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>AED) <img decoding=\"async\" style=\"height: 14px; width: 12px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image035.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BEC) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ABE) <img decoding=\"async\" style=\"height: 14px; width: 12px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image035.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>CDE)<\/p>\n<p style=\"text-align: justify;\">Hence proved.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 9.4<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"7_P_and_Q_are_respectively_the_mid-points_of_sides_AB_and_BC_or_a_triangle_ABC_and_R_is_the_mid-point_of_AP_show_that\"><\/span><strong>7. P and Q are respectively the mid-points of sides AB and BC or a triangle ABC and R is the mid-point of AP, show that:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(i) ar (PRQ) = <\/strong><img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/><strong> ar (ARC)<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) ar (RQC) = <\/strong><img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image044.png\" \/><strong> ar (ABC)<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) ar (PBQ) = ar (ARC)<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i)<\/strong> PC is the median of <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ABC.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image002.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BPC) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>APC) \u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\">RC is the median of <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>APC.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image002.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ARC) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>APC) \u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\">[Median divides the triangle into two triangles of equal area]\n<p style=\"text-align: justify;\">PQ is the median of <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BPC.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 1612\" style=\"height: 191px; width: 231px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image045.jpg\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image002.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>PQC) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BPC) \u2026\u2026\u2026.(iii)<\/p>\n<p style=\"text-align: justify;\">From eq. (i) and (iii), we get,<\/p>\n<p style=\"text-align: justify;\">ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>PQC) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>APC) \u2026\u2026\u2026.(iv)<\/p>\n<p style=\"text-align: justify;\">From eq. (ii) and (iv), we get,<\/p>\n<p style=\"text-align: justify;\">ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>PQC) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ARC) \u2026\u2026\u2026.(v)<\/p>\n<p style=\"text-align: justify;\">We are given that P and Q are the mid-points of AB and BC respectively.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image002.png\" \/>PQ <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image003.png\" \/> AC and PA = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> AC<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>APQ) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>PQC) \u2026\u2026\u2026.(vi) [triangles between same parallel are equal in area]\n<p style=\"text-align: justify;\">From eq. (v) and (vi), we get<\/p>\n<p style=\"text-align: justify;\">ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>APQ) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ARC) \u2026\u2026\u2026.(vii)<\/p>\n<p style=\"text-align: justify;\">R is the mid-point of AP. Therefore RQ is the median of <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>APQ.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image002.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>PRQ) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>APQ) \u2026\u2026\u2026.(viii)<\/p>\n<p style=\"text-align: justify;\">From (vii) and (viii), we get,<\/p>\n<p style=\"text-align: justify;\">ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>PRQ) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ARC)<\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> PQ is the median of <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BPC<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image002.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>PQC) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BPC) = <img decoding=\"async\" style=\"height: 41px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image046.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ABC) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image019.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ABC) \u2026\u2026\u2026.(ix)<\/p>\n<p style=\"text-align: justify;\">Also ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>PRC) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>APC) [Using (iv)]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>PRC) = <img decoding=\"async\" style=\"height: 41px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image046.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ABC) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image019.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ABC) \u2026\u2026\u2026.(x)<\/p>\n<p style=\"text-align: justify;\">Adding eq. (ix) and (x), we get,<\/p>\n<p style=\"text-align: justify;\">ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>PQC) + ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>PRC) = <img decoding=\"async\" style=\"height: 45px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image047.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ABC)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/>ar (quad. PQCR) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ABC) \u2026\u2026\u2026.(xi)<\/p>\n<p style=\"text-align: justify;\">Subtracting ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>PRQ) from the both sides,<\/p>\n<p style=\"text-align: justify;\">ar (quad. PQCR) \u2013 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>PRQ) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ABC) \u2013 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>PRQ)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>RQC) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ABC) \u2013 <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ARC) [Using result (i)]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ARC) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ABC) \u2013 <img decoding=\"async\" style=\"height: 41px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image048.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>APC)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>RQC) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ABC) \u2013 <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image019.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>APC)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>RQC) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ABC) \u2013 <img decoding=\"async\" style=\"height: 41px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image049.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ABC) [PC is median of <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ABC]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>RQC) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ABC) \u2013 <img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image021.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ABC)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>RQC) = <img decoding=\"async\" style=\"height: 45px; width: 55px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image050.png\" \/> <img decoding=\"async\" style=\"height: 14px; width: 12px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image035.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ABC)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>RQC) = <img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image044.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ABC)<\/p>\n<p style=\"text-align: justify;\"><strong>(iii)<\/strong> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>PRQ) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ARC) [Using result (i)] <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/> 2 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>PRQ) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ARC) ..(xii)<\/p>\n<p style=\"text-align: justify;\">ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>PRQ) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>APQ) [RQ is the median of <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>APQ] \u2026\u2026\u2026.(xiii)<\/p>\n<p style=\"text-align: justify;\">But ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>APQ) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>PQC) [Using reason of eq. (vi)] \u2026\u2026\u2026.(xiv)<\/p>\n<p style=\"text-align: justify;\">From eq. (xiii) and (xiv), we get,<\/p>\n<p style=\"text-align: justify;\">ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>PRQ) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>PQC) \u2026\u2026\u2026.(xv)<\/p>\n<p style=\"text-align: justify;\">But ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BPQ) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>PQC) [PQ is the median of <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BPC] \u2026\u2026\u2026.(xvi)<\/p>\n<p style=\"text-align: justify;\">From eq. (xv) and (xvi), we get,<\/p>\n<p style=\"text-align: justify;\">ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>PRQ) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BPQ) \u2026\u2026\u2026.(xvii)<\/p>\n<p style=\"text-align: justify;\">Now from (xii) and (xvii), we get,<\/p>\n<p style=\"text-align: justify;\">2<img decoding=\"async\" style=\"height: 45px; width: 101px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image051.png\" \/> = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ARC) <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>BPQ) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ARC)<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 9.4<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"8_In_figure_ABC_is_a_right_triangle_right_angled_at_A_BCED_ACFG_and_ABMN_are_squares_on_the_sides_BC_CA_and_AB_respectively_Line_segment_AXDE_meets_BC_at_Y_Show_that\"><\/span><strong>8. In figure, ABC is a right triangle right angled at A. BCED, ACFG and ABMN are squares on the sides BC, CA and AB respectively. Line segment AX<\/strong><img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image009.png\" \/><strong>DE meets BC at Y. Show that:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(i) <\/strong><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/><strong>MBC <\/strong><img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image052.png\" \/><strong>ABD<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) ar (BYXD) = 2 ar (MBC)<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) ar (BYXD) = ar (ABMN)<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iv) <\/strong><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/><strong>FCB <\/strong><img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image052.png\" \/><strong>ACE<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(v) ar (CYXE) = 2 ar (FCB)<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(vi) ar (CYXE) = ar (ACFG)<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(vii) ar (BCED) = ar (ABMN) + ar (ACFG)<\/strong><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 1615\" style=\"height: 185px; width: 166px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image053.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong> <strong>(i)<\/strong> <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image017.png\" \/>ABM = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image017.png\" \/>CBD = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image054.png\" \/><\/p>\n<p style=\"text-align: justify;\">Adding <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image017.png\" \/>ABC both sides, we get,<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image017.png\" \/>ABM + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image017.png\" \/>ABC = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image017.png\" \/>CBD + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image017.png\" \/>ABC <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image017.png\" \/>MBC = ABD \u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\">Now in <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>MBC and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ABD,<\/p>\n<p style=\"text-align: justify;\">MB = AB [equal sides of square ABMN]\n<p style=\"text-align: justify;\">BC = BD [sides of square BCED]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image017.png\" \/>MBC = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image017.png\" \/>ABD [proved above]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image002.png\" \/> <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/> MBC <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image052.png\" \/>ABD [By SAS congruency]\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"ii_From_above_MBC_ABD\"><\/span><strong>(ii)<\/strong> From above, <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>MBC <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image052.png\" \/>ABD<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>MBC) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ABD) <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>MBC) = ar (trap. ABDX) \u2013 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ADX)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>MBC) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> (BD + AX) BY \u2013 <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> DX.AX<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>MBC) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> BD.BY + <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> AX.BY \u2013 <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> DX.AX<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>MBC) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> BD.BY + <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> AX (BY \u2013 DX)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>MBC) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> BD.BY + <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> AX. 0 [BY = DX]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>MBC) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> BD.BY<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/> 2 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>MBC) = BD.BY <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/>2 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>MBC) = ar (rect. BYXD)<\/p>\n<p style=\"text-align: justify;\">Hence ar (BYXD) = 2 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>MBC)<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"iii_Join_AM_ABMN_is_a_square\"><\/span><strong>(iii)<\/strong> Join AM. ABMN is a square.<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\">Therefore, NA <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image003.png\" \/> MB <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/>AC <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image003.png\" \/> MB<\/p>\n<p style=\"text-align: justify;\">Now <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>AMB and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>MBC are on the same base and between the same parallels MB and AC.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image002.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>AMB) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>MBC) \u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\">From result (ii), we have ar (BYXD) = 2 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>MBC) \u2026\u2026\u2026.(iii)<\/p>\n<p style=\"text-align: justify;\">Using eq. (ii) and (iii), we get, ar (BYXD) = 2 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>AMB)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/> ar (BYXD) = ar (square ABMN)<\/p>\n<p style=\"text-align: justify;\">[Diagonal AM of square ABMN divides it in two triangles of equal area]\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"iv_In_FCB_and_ACE\"><\/span><strong>(iv)<\/strong> In <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>FCB and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ACE,<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\">FC = AC [sides of square ACFG]\n<p style=\"text-align: justify;\">BC = CE [sides of square BCED]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image017.png\" \/>BCF = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image017.png\" \/>ACE [<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image004.png\" \/> <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image017.png\" \/>ACF = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image017.png\" \/>BCE = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image054.png\" \/>]\n<p style=\"text-align: justify;\">Adding <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image017.png\" \/>ACB both sides,<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image017.png\" \/>BCF + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image017.png\" \/>ACB = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image017.png\" \/>ACE + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image017.png\" \/>ACB <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image017.png\" \/>BCF = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image017.png\" \/>ACE<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image002.png\" \/> <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>FCB <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image052.png\" \/>ACE [By SAS congruency]\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"v_From_iv_we_have_FCB_ACE\"><\/span><strong>(v)<\/strong> From (iv), we have, <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>FCB <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image052.png\" \/>ACE<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>FCB) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ACE) <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>FCB) = ar (trap. ACEX) \u2013 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>AEX)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>FCB) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> (CE + AX) CY \u2013 <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> XE.AX<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>FCB) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> CE.CY + <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> AX.CY \u2013 <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> XE.AX<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>FCB) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> CE.CY + <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> AX (CY \u2013 XE)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>FCB) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> CE.CY + <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> AX. 0 [CY = XE]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>FCB) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image020.png\" \/> CE.CY<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/> 2 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>FCB) = CE.CY <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/>2 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>FCB) = ar (rect. CYXE)<\/p>\n<p style=\"text-align: justify;\">Hence ar (BYXD) = 2 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>FCB)<\/p>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 9.4<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"vi_Join_AF_ACFG_is_a_square\"><\/span><strong>(vi)<\/strong> Join AF. ACFG is a square.<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image002.png\" \/>FC <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image003.png\" \/> AG <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/>FC <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image003.png\" \/> AB<\/p>\n<p style=\"text-align: justify;\">Now <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ACF and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>FCB are on the same base FC and between the same parallels FC and AB.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image002.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ACF) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>FCB) \u2026\u2026\u2026.(v)<\/p>\n<p style=\"text-align: justify;\">From result (v), we get, ar (CYXE) = 2 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>FCB) \u2026\u2026\u2026.(vi)<\/p>\n<p style=\"text-align: justify;\">Using eq. (v) in (vi), we get, ar (CYXE) = 2 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image007.png\" \/>ACF)<\/p>\n<p style=\"text-align: justify;\">Diagonal AF of square ACFG divides it in two triangles of equal area.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image002.png\" \/> ar (CYXE) = ar (sq. ACFG) \u2026\u2026\u2026.(vii)<\/p>\n<p style=\"text-align: justify;\"><strong>(vii)<\/strong> Adding eq. (iv) and (vii), we get,<\/p>\n<p style=\"text-align: justify;\">ar (BYXD) + ar (CYXE) = ar (ABMN) + ar (ACFG)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.4\/image005.png\" \/> ar (BCED) = ar (ABMN) + ar (ACFG)<\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_9_Maths_Exercise_94\"><\/span>NCERT Solutions for Class 9 Maths Exercise 9.4<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>NCERT Solutions for Class 9 Maths Exercise 9.4 PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 9 Maths includes text book solutions from Mathematics Book. NCERT Solutions for CBSE Class 9 Maths have total 15 chapters. 9 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 9 solutions PDF and Maths ncert class 9 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_app_for_Class_9\"><\/span>CBSE app for Class 9<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To download NCERT Solutions for Class 9 Maths, Computer Science, Home Science,Hindi ,English, Social Science do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through\u00a0<a href=\"https:\/\/play.google.com\/store\/apps\/details?id=in.techchefs.MyCBSEGuide&amp;referrer=utm_source%3Dmycbse_bottom%26utm_medium%3Dtext%26utm_campaign%3Dmycbseads\"><strong>the best app for CBSE students<\/strong><\/a>\u00a0and myCBSEguide website.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions for Class 9 Maths Exercise 9.4 book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. 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