{"id":5000,"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-9-3\/"},"modified":"2018-06-18T16:14:20","modified_gmt":"2018-06-18T10:44:20","slug":"ncert-solutions-for-class-9-maths-exercise-9-3","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-9-3\/","title":{"rendered":"NCERT Solutions for Class 9 Maths Exercise 9.3"},"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-9-3\/#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-9-3\/#1_In_figure_E_is_any_point_on_median_AD_of_a_ABC_Show_that_ar_ABE_ar_ACE\" >1. In figure, E is any point on median AD of a ABC. Show that ar (ABE) = ar (ACE).<\/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-9-3\/#2_In_a_triangle_ABC_E_is_the_mid-point_of_median_AD_Show_that_ar_BED_ar_ABC\" >2. In a triangle ABC, E is the mid-point of median AD. Show that ar (BED) =  ar (ABC).<\/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-9-3\/#3_Show_that_the_diagonals_of_a_parallelogram_divide_it_into_four_triangles_of_equal_area\" >3. Show that the diagonals of a parallelogram divide it into four triangles of equal area.<\/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-9-3\/#4_In_figure_ABC_and_ABD_are_two_triangles_on_the_same_base_AB_If_line-segment_CD_is_bisected_by_AB_at_O_show_that_ar_ABC_ar_ABD\" >4. In figure, ABC and ABD are two triangles on the same base AB. If line-segment CD is bisected by AB at O, show that ar (ABC) = ar (ABD).<\/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-9-3\/#5_D_E_and_F_are_respectively_the_mid-points_of_the_sides_BC_CA_and_AB_of_a_ABC_Show_that\" >5. D, E and F are respectively the mid-points of the sides BC, CA and AB of a ABC. 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-9-3\/#Again_E_is_the_mid-point_of_AC_and_D_is_the_mid-point_of_BC\" >Again E is the mid-point of AC and D is the mid-point of BC.<\/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-9-3\/#6_In_figure_diagonals_AC_and_BD_of_quadrilateral_ABCD_intersect_at_O_such_that_OB_OD_If_AB_CD_then_show_that\" >6. In figure, diagonals AC and BD of quadrilateral ABCD intersect at O such that OB = OD. If AB = CD, then 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-9-3\/#CD_AB_Given\" >CD = AB [Given]<\/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-9-3\/#7_D_and_E_are_points_on_sides_AB_and_AC_respectively_of_ABC_such_that_ar_DBC_ar_EBC_Prove_that_DEBC\" >7. D and E are points on sides AB and AC respectively of ABC such that ar (DBC) = ar (EBC). Prove that DEBC.<\/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-9-3\/#8_XY_is_a_line_parallel_to_side_BC_of_triangle_ABC_If_BEAC_and_CFAB_meet_XY_at_E_and_F_respectively_show_that_ar_ABE_ar_ACF\" >8. XY is a line parallel to side BC of triangle ABC. If BEAC and CFAB meet XY at E and F respectively, show that ar (ABE) = ar (ACF).<\/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-9-3\/#9_The_side_AB_of_parallelogram_ABCD_is_produced_to_any_point_P_A_line_through_A_and_parallel_to_CP_meets_CB_produced_at_Q_and_then_parallelogram_PBQR_is_completed_Show_that_ar_ABCD_ar_PBQR\" >9. The side AB of parallelogram ABCD is produced to any point P. A line through A and parallel to CP meets CB produced at Q and then parallelogram PBQR is completed. Show that ar (ABCD) = ar (PBQR).<\/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-9-3\/#10_Diagonals_AC_and_BD_of_a_trapezium_ABCD_with_ABDC_intersect_each_other_at_O_Prove_that_arAOD_ar_BOC\" >10. Diagonals AC and BD of a trapezium ABCD with ABDC intersect each other at O. Prove that ar(AOD) = ar (BOC).<\/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-9-3\/#12_A_villager_Itwaari_has_a_plot_of_land_of_the_shape_of_quadrilateral_The_Gram_Panchyat_of_two_villages_decided_to_take_over_some_portion_of_his_plot_from_one_of_the_corners_to_construct_a_health_centre_Itwaari_agrees_to_the_above_personal_with_the_condition_that_he_should_be_given_equal_amount_of_land_in_lieu_of_his_land_adjoining_his_plot_so_as_to_form_a_triangular_plot_Explain_how_this_proposal_will_be_implemented\" >12. A villager Itwaari has a plot of land of the shape of quadrilateral. The Gram Panchyat of two villages decided to take over some portion of his plot from one of the corners to construct a health centre. Itwaari agrees to the above personal with the condition that he should be given equal amount of land in lieu of his land adjoining his plot so as to form a triangular plot. Explain how this proposal will be implemented.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-9-3\/#13_ABCD_is_a_trapezium_with_ABDC_A_line_parallel_to_AC_intersects_AB_at_X_and_BC_at_Y_Prove_that_ar_ADX_ar_ACY\" >13. ABCD is a trapezium with ABDC. A line parallel to AC intersects AB at X and BC at Y. Prove that ar (ADX) = ar (ACY).<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-9-3\/#14_In_figure_APBQCR_Prove_that_ar_AQC_ar_PBR\" >14. In figure, APBQCR. Prove that ar (AQC) = ar (PBR).<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-9-3\/#16_In_figure_ar_DRC_ar_DPC_and_ar_BDP_ar_ARC_Show_that_both_the_quadrilaterals_ABCD_and_DCPR_are_trapeziums\" >16. In figure, ar (DRC) = ar (DPC) and ar (BDP) = ar (ARC). Show that both the quadrilaterals ABCD and DCPR are trapeziums.<\/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-18\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-9-3\/#NCERT_Solutions_for_Class_9_Maths_Exercise_93\" >NCERT Solutions for Class 9 Maths Exercise 9.3<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-9-3\/#CBSE_app_for_Class_9\" >CBSE app for Class 9<\/a><\/li><\/ul><\/nav><\/div>\n<p>NCERT Solutions for Class 9 Maths Exercise 9.3 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 9.3\" width=\"171\" height=\"220\" \/><\/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_In_figure_E_is_any_point_on_median_AD_of_a_ABC_Show_that_ar_ABE_ar_ACE\"><\/span><strong>1. In figure, E is any point on median AD of a <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABC. Show that ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABE) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ACE).<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 23\" style=\"height: 118px; width: 151px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image002.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\/Ex9.3\/image001.png\" \/>ABC, AD is a median.<\/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\/Ex9.3\/image001.png\" \/>ABD) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ACD) \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\/Ex9.3\/image003.png\" \/> Median divides a <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/> into two <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>s of equal area]\n<p style=\"text-align: justify;\">Again in <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>EBC, ED is a median<\/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\/Ex9.3\/image001.png\" \/>EBD) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ECD) \u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\">Subtracting eq. (ii) from (i),<\/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\/Ex9.3\/image001.png\" \/>ABD) \u2013 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>EBD) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ACD) \u2013 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ECD)<\/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\/Ex9.3\/image004.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABE) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ACE)<\/p>\n<hr \/>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"2_In_a_triangle_ABC_E_is_the_mid-point_of_median_AD_Show_that_ar_BED_ar_ABC\"><\/span><strong>2. In a triangle ABC, E is the mid-point of median AD. Show that ar (BED) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image005.png\" \/> ar (ABC).<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. Given<\/strong>: A <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABC, AD is the median and E is the mid-point of median AD.<\/p>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 26\" style=\"height: 130px; width: 169px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image006.jpg\" \/><\/strong><\/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\/Ex9.3\/image001.png\" \/>BED) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image005.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABC)<\/p>\n<p style=\"text-align: justify;\"><strong>Proof<\/strong>: In <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABC, AD 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\/Ex9.3\/image007.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABD) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ADC)<\/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\/Ex9.3\/image003.png\" \/> Median divides a <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/> into two <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>s of equal area]\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\/Ex9.3\/image004.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABD) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image008.png\" \/> ar (ABC) \u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\">In <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABD, BE 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\/Ex9.3\/image007.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>BED) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>BAE)<\/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\/Ex9.3\/image004.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>BED) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image008.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABD)<\/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\/Ex9.3\/image004.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>BED) = <img decoding=\"async\" style=\"height: 41px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image009.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABC) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image005.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABC)<\/p>\n<hr \/>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"3_Show_that_the_diagonals_of_a_parallelogram_divide_it_into_four_triangles_of_equal_area\"><\/span><strong>3. Show that the diagonals of a parallelogram divide it into four triangles of equal area.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 27\" style=\"height: 131px; width: 208px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image010.jpg\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let parallelogram be ABCD and its diagonals AC and BD intersect each other at O.<\/p>\n<p style=\"text-align: justify;\">In <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABC and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ADC,<\/p>\n<p style=\"text-align: justify;\">AB = DC [Opposite sides of a parallelogram]\n<p style=\"text-align: justify;\">BC = AD [Opposite sides of a parallelogram]\n<p style=\"text-align: justify;\">And AC = AC [Common]\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\/Ex9.3\/image007.png\" \/> <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABC <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image011.png\" \/> <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>CDA [By SSS congruency]\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\/Ex9.3\/image007.png\" \/> O is the mid-point of bisection.<\/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\/Ex9.3\/image001.png\" \/>ADC, DO 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\/Ex9.3\/image007.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>AOD) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>COD) \u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\">[Median divides a triangle into two equal areas]\n<p style=\"text-align: justify;\">Similarly, in <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABC, OB 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\/Ex9.3\/image007.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>AOB) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>BOC) \u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\">And in <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>AOB and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>AOD, AO 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\/Ex9.3\/image007.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>AOB) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>AOD) \u2026\u2026\u2026.(iii)<\/p>\n<p style=\"text-align: justify;\">From eq. (i), (ii) and (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\/Ex9.3\/image001.png\" \/>AOB) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>AOD) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>BOC) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>COD)<\/p>\n<p style=\"text-align: justify;\">Thus diagonals of parallelogram divide it into four triangles of equal area.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 9.3<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"4_In_figure_ABC_and_ABD_are_two_triangles_on_the_same_base_AB_If_line-segment_CD_is_bisected_by_AB_at_O_show_that_ar_ABC_ar_ABD\"><\/span><strong>4. In figure, ABC and ABD are two triangles on the same base AB. If line-segment CD is bisected by AB at O, show that ar (ABC) = ar (ABD).<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 24\" style=\"height: 140px; width: 124px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image012.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Draw CM<img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image013.png\" \/>AB and DN<img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image013.png\" \/>AB.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 28\" style=\"height: 145px; width: 151px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image014.png\" \/><\/p>\n<p style=\"text-align: justify;\">In <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>CMO and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>DNO,<\/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\/Ex9.3\/image015.png\" \/>CMO = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image015.png\" \/>DNO = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image016.png\" \/> [By construction]\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\/Ex9.3\/image015.png\" \/>COM = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image015.png\" \/>DON [Vertically opposite]\n<p style=\"text-align: justify;\">OC = OD [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\/Ex9.3\/image007.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>CMO <img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image011.png\" \/> <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>DNO [By ASA 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\/Ex9.3\/image003.png\" \/> AM = DN [By CPCT] \u2026\u2026(i)<\/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\/Ex9.3\/image001.png\" \/>ABC) = <img decoding=\"async\" style=\"height: 42px; width: 90px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image017.png\" \/> \u2026\u2026\u2026.(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\/Ex9.3\/image001.png\" \/>ADB) = <img decoding=\"async\" style=\"height: 42px; width: 88px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image018.png\" \/> \u2026\u2026\u2026.(iii)<\/p>\n<p style=\"text-align: justify;\">Using eq. (i) and (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\/Ex9.3\/image001.png\" \/>ADB) = <img decoding=\"async\" style=\"height: 42px; width: 90px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image017.png\" \/>\u2026\u2026\u2026.(iv)<\/p>\n<p style=\"text-align: justify;\">From eq. (ii) 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\/Ex9.3\/image001.png\" \/>ABC) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ADB)<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 9.3<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"5_D_E_and_F_are_respectively_the_mid-points_of_the_sides_BC_CA_and_AB_of_a_ABC_Show_that\"><\/span><strong>5. D, E and F are respectively the mid-points of the sides BC, CA and AB of a <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABC. Show that:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(i) BDEF is a parallelogram.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) ar (DEF) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image005.png\" \/> ar (ABC)<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) ar (BDEF) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image008.png\" \/> ar (ABC)<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i)<\/strong> F is the mid-point of AB and E is the mid-point of AC.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 29\" style=\"height: 144px; width: 168px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image019.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\/Ex9.3\/image007.png\" \/> FE<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>BC and FE = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image008.png\" \/> BD<\/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\/Ex9.3\/image003.png\" \/> Line joining the mid-points of two sides of a triangle is parallel to the third and half of it]\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\/Ex9.3\/image004.png\" \/> FE<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>BD [BD is the part of BC]\n<p style=\"text-align: justify;\">And FE = BD<\/p>\n<p style=\"text-align: justify;\">Also, D is the mid-point of 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\/Ex9.3\/image007.png\" \/> BD = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image008.png\" \/> BC<\/p>\n<p style=\"text-align: justify;\">And FE<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>BC and FE = BD<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Again_E_is_the_mid-point_of_AC_and_D_is_the_mid-point_of_BC\"><\/span>Again E is the mid-point of AC and D is the mid-point of BC.<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\/Ex9.3\/image007.png\" \/> DE<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>AB and DE = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image008.png\" \/> AB<\/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\/Ex9.3\/image004.png\" \/> DE<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>AB [BF is the part of AB]\n<p style=\"text-align: justify;\">And DE = BF<\/p>\n<p style=\"text-align: justify;\">Again F is the mid-point of 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\/Ex9.3\/image007.png\" \/> BF = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image008.png\" \/> AB<\/p>\n<p style=\"text-align: justify;\">But DE = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image008.png\" \/> 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\/Ex9.3\/image007.png\" \/> DE = BF<\/p>\n<p style=\"text-align: justify;\">Now we have FE<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>BD and DE<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>BF<\/p>\n<p style=\"text-align: justify;\">And FE = BD and DE = BF<\/p>\n<p style=\"text-align: justify;\">Therefore, BDEF is a parallelogram.<\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> BDEF 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\/Ex9.3\/image007.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>BDF) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>DEF) \u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\">[diagonals of parallelogram divides it in two triangles of equal area]\n<p style=\"text-align: justify;\">DCEF is also 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\/Ex9.3\/image007.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>DEF) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>DEC) \u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\">Also, AEDF is also 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\/Ex9.3\/image007.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>AFE) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>DEF) \u2026\u2026\u2026.(iii)<\/p>\n<p style=\"text-align: justify;\">From eq. (i), (ii) and (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\/Ex9.3\/image001.png\" \/>DEF) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>BDF) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>DEC) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>AFE) \u2026\u2026\u2026.(iv)<\/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\/Ex9.3\/image001.png\" \/>ABC) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>DEF) + ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>BDF) + ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>DEC) + ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>AFE) \u2026\u2026\u2026.(v)<\/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\/Ex9.3\/image004.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABC) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>DEF) + ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>DEF) + ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>DEF) + ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>DEF)<\/p>\n<p style=\"text-align: justify;\">[Using (iv) &amp; (v)]\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\/Ex9.3\/image004.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABC) = 4 <img decoding=\"async\" style=\"height: 14px; width: 12px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image021.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>DEF)<\/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\/Ex9.3\/image004.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>DEF) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image005.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABC)<\/p>\n<p style=\"text-align: justify;\"><strong>(iii)<\/strong> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>gm BDEF) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>BDF) + ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>DEF) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>DEF) + ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>DEF) [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\/Ex9.3\/image004.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>gm BDEF) = 2 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>DEF)<\/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\/Ex9.3\/image004.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>gm BDEF) = <img decoding=\"async\" style=\"height: 42px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image022.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.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\/Ex9.3\/image004.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>gm BDEF) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image008.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABC)<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 9.3<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"6_In_figure_diagonals_AC_and_BD_of_quadrilateral_ABCD_intersect_at_O_such_that_OB_OD_If_AB_CD_then_show_that\"><\/span><strong>6. In figure, diagonals AC and BD of quadrilateral ABCD intersect at O such that OB = OD. If AB = CD, then show that:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 25\" style=\"height: 101px; width: 164px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image023.png\" \/> <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(i) ar (DOC) = ar (AOB) <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) ar (DCB) = ar (ACB) <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) DA<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>CB or ABCD is a parallelogram.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i)<\/strong> Draw BM <img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image013.png\" \/> AC and DN <img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image013.png\" \/> AC.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 30\" style=\"height: 126px; width: 172px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image024.jpg\" \/><\/p>\n<p style=\"text-align: justify;\">In <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>DON and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>BOM,<\/p>\n<p style=\"text-align: justify;\">OD = OB [Given]\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\/Ex9.3\/image015.png\" \/>DNO = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image015.png\" \/>BMO = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image016.png\" \/> [By construction]\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\/Ex9.3\/image015.png\" \/>DON = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image015.png\" \/>BOM [Vertically opposite]\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\/Ex9.3\/image007.png\" \/> <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>DON <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image025.png\" \/>BOM [By RHS congruency]\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\/Ex9.3\/image004.png\" \/> DN = BM [By CPCT]\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\/Ex9.3\/image001.png\" \/>DON) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>BOM) \u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\">Again, In <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>DCN and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABM,<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"CD_AB_Given\"><\/span>CD = AB [Given]<span class=\"ez-toc-section-end\"><\/span><\/h6>\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\/Ex9.3\/image015.png\" \/>DNC = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image015.png\" \/>BMA = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image016.png\" \/> [By construction]\n<p style=\"text-align: justify;\">DN = BM [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\/Ex9.3\/image007.png\" \/> <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>DCN <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image025.png\" \/>BAM [By RHS 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\/Ex9.3\/image007.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>DCN) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>BAM) \u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\">Adding 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\/Ex9.3\/image001.png\" \/>DON) + ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>DCN) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>BOM) + ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>BAM)<\/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\/Ex9.3\/image004.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>DOC) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>AOB)<\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> Since ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>DOC) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>AOB)<\/p>\n<p style=\"text-align: justify;\">Adding ar <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>BOC both 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\/Ex9.3\/image001.png\" \/>DOC) + ar <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>BOC = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>AOB) + ar <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>BOC<\/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\/Ex9.3\/image004.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>DCB) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ACB)<\/p>\n<p style=\"text-align: justify;\"><strong>(iii)<\/strong> Since ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>DCB) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ACB)<\/p>\n<p style=\"text-align: justify;\">Therefore, these two triangles in addition to be on the same base CB lie between two same parallels CB and DA.<\/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\/Ex9.3\/image007.png\" \/> DA<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>CB<\/p>\n<p style=\"text-align: justify;\">Now AB = CD and DA<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>CB<\/p>\n<p style=\"text-align: justify;\">Therefore, ABCD is a parallelogram.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 9.3<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"7_D_and_E_are_points_on_sides_AB_and_AC_respectively_of_ABC_such_that_ar_DBC_ar_EBC_Prove_that_DEBC\"><\/span><strong>7. D and E are points on sides AB and AC respectively of <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABC such that ar (DBC) = ar (EBC). Prove that DE<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>BC.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Given: ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>DBC) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>EBC)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 146px; width: 142px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image026.png\" \/><\/p>\n<p style=\"text-align: justify;\">Since two triangles of equal area have common base BC.<\/p>\n<p style=\"text-align: justify;\">Therefore, DE<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>BC [<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image003.png\" \/> Two triangles having same base (or equal bases) and equal areas lie between the same parallel]\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 9.3<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"8_XY_is_a_line_parallel_to_side_BC_of_triangle_ABC_If_BEAC_and_CFAB_meet_XY_at_E_and_F_respectively_show_that_ar_ABE_ar_ACF\"><\/span><strong>8. XY is a line parallel to side BC of triangle ABC. If BE<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>AC and CF<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>AB meet XY at E and F respectively, show that ar (ABE) = ar (ACF).<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABE and parallelogram BCYE lie on the same base BE and between the same parallels BE and AC.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 31\" style=\"height: 130px; width: 165px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image027.png\" \/><\/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\/Ex9.3\/image007.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABE) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image008.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>gm BCYE) \u2026\u2026\u2026.(i)<\/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\/Ex9.3\/image001.png\" \/>ACF and <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>gm BCFX lie on the same base CF and between same parallel BX and CF.<\/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\/Ex9.3\/image007.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ACF) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image008.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>gm BCFX) \u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\">But <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>gm BCYE and <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>gm BCFX lie on the same base BC and between the same parallels BC and EF.<\/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\/Ex9.3\/image007.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>gm BCYE) = ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>gm BCFX) \u2026\u2026\u2026.(iii)<\/p>\n<p style=\"text-align: justify;\">From eq. (i), (ii) 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\/Ex9.3\/image001.png\" \/>ABE) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ACF)<\/p>\n<hr \/>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"9_The_side_AB_of_parallelogram_ABCD_is_produced_to_any_point_P_A_line_through_A_and_parallel_to_CP_meets_CB_produced_at_Q_and_then_parallelogram_PBQR_is_completed_Show_that_ar_ABCD_ar_PBQR\"><\/span><strong>9. The side AB of parallelogram ABCD is produced to any point P. A line through A and parallel to CP meets CB produced at Q and then parallelogram PBQR is completed. Show that ar (ABCD) = ar (PBQR).<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. Given<\/strong>: ABCD is a parallelogram, CP<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>AQ and PBQR is a parallelogram.<\/p>\n<p style=\"text-align: justify;\"><strong>To prove<\/strong>: ar (ABCD) = ar (PBQR)<\/p>\n<p style=\"text-align: justify;\"><strong>Construction<\/strong>: Join AC and QP.<\/p>\n<p style=\"text-align: justify;\"><strong>Proof<\/strong>: Since AQ<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>CP<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 1569\" style=\"height: 167px; width: 142px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image028.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\/Ex9.3\/image007.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>AQC) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>AQP)<\/p>\n<p style=\"text-align: justify;\">[Triangles on the same base and between the same parallels are equal in area]\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\/Ex9.3\/image001.png\" \/>ABQ) from both sides, 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\/Ex9.3\/image001.png\" \/>AQC \u2013 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABQ) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>AQP) \u2013 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABQ)<\/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\/Ex9.3\/image004.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABC) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>QBP) \u2026\u2026\u2026.(i)<\/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\/Ex9.3\/image001.png\" \/>ABC) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image008.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>gm ABCD)<\/p>\n<p style=\"text-align: justify;\">[Diagonal divides a parallelogram in two parts of equal area]\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\/Ex9.3\/image001.png\" \/>PQB) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image008.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>gm PBQR)<\/p>\n<p style=\"text-align: justify;\">From eq. (i), (ii) and (iii), we get<\/p>\n<p style=\"text-align: justify;\">ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>gm ABCD) = ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>gm PBQR)<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 9.3<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"10_Diagonals_AC_and_BD_of_a_trapezium_ABCD_with_ABDC_intersect_each_other_at_O_Prove_that_arAOD_ar_BOC\"><\/span><strong>10. Diagonals AC and BD of a trapezium ABCD with AB<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>DC intersect each other at O. Prove that ar(AOD) = ar (BOC). <\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 22\" style=\"height: 141px; width: 167px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image029.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABD and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABC lie on the same base AB and between the same parallels AB and DC.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 118px; width: 202px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image030.png\" \/><\/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\/Ex9.3\/image007.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABD) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABC)<\/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\/Ex9.3\/image001.png\" \/>AOB) from both 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\/Ex9.3\/image001.png\" \/>ABD) \u2013 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>AOB)<\/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\/Ex9.3\/image001.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\/Ex9.3\/image001.png\" \/>AOB)<\/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\/Ex9.3\/image004.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>AOD) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>BOC)<\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>11. In figure, ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F. Show that:<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(i) ar (ACB = ar (ACF)<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) ar (AEDF) = ar (ABCDE)<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i)<\/strong> Given that BF<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>AC<\/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\/Ex9.3\/image001.png\" \/>ACB and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ACF lie on the same base AC and between the same parallels AC and BF.<\/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\/Ex9.3\/image007.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ACB) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ACF) \u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> Now ar (ABCDE) = ar (trap. AEDC) + ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABC) \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\/Ex9.3\/image004.png\" \/> ar (ABCDE) = ar (trap. AEDC) + ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ACF) = ar (quad. AEDF) [Using (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\/Ex9.3\/image004.png\" \/> ar (AEDF) = ar (ABCDE)<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 9.3<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"12_A_villager_Itwaari_has_a_plot_of_land_of_the_shape_of_quadrilateral_The_Gram_Panchyat_of_two_villages_decided_to_take_over_some_portion_of_his_plot_from_one_of_the_corners_to_construct_a_health_centre_Itwaari_agrees_to_the_above_personal_with_the_condition_that_he_should_be_given_equal_amount_of_land_in_lieu_of_his_land_adjoining_his_plot_so_as_to_form_a_triangular_plot_Explain_how_this_proposal_will_be_implemented\"><\/span><strong>12. A villager Itwaari has a plot of land of the shape of quadrilateral. The Gram Panchyat of two villages decided to take over some portion of his plot from one of the corners to construct a health centre. Itwaari agrees to the above personal with the condition that he should be given equal amount of land in lieu of his land adjoining his plot so as to form a triangular plot. Explain how this proposal will be implemented.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let Itwari has land in shape of quadrilateral PQRS.<\/p>\n<p style=\"text-align: justify;\">Draw a line through 5 parallel to PR, which meets QR produced at M.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 1574\" style=\"height: 191px; width: 234px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image031.jpg\" \/><\/p>\n<p style=\"text-align: justify;\">Let diagonals PM and RS of new formed quadrilateral intersect each other at point N.<\/p>\n<p style=\"text-align: justify;\">We have PR<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>SM [By construction]\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\/Ex9.3\/image007.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>PRS) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>PMR)<\/p>\n<p style=\"text-align: justify;\">[Triangles on the same base and same parallel are equal in area]\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\/Ex9.3\/image001.png\" \/>PNR) from both 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\/Ex9.3\/image001.png\" \/>PRS) \u2013 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>PNR) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>PMR) \u2013 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>PNR)<\/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\/Ex9.3\/image004.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>PSN) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>MNR)<\/p>\n<p style=\"text-align: justify;\">It implies that Itwari will give corner triangular shaped plot PSN to the Grampanchayat for health centre and will take equal amount of land (denoted by <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>MNR) adjoining his plot so as to form a triangular plot PQM.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 9.3<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"13_ABCD_is_a_trapezium_with_ABDC_A_line_parallel_to_AC_intersects_AB_at_X_and_BC_at_Y_Prove_that_ar_ADX_ar_ACY\"><\/span><strong>13. ABCD is a trapezium with AB<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>DC. A line parallel to AC intersects AB at X and BC at Y. Prove that ar (ADX) = ar (ACY).<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Join CX, <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ADX and ACX lie on the same base XA and between the same parallels XA and DC.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 1572\" style=\"height: 121px; width: 211px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image032.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\/Ex9.3\/image007.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ADX) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ACX) \u2026\u2026\u2026.(i)<\/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\/Ex9.3\/image001.png\" \/>ACX and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ACY lie on the same base<\/p>\n<p style=\"text-align: justify;\">AC and between same parallels CY and XA.<\/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\/Ex9.3\/image007.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ACX) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ACY) \u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\">From (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\/Ex9.3\/image001.png\" \/>ADX) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ACY)<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 9.3<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"14_In_figure_APBQCR_Prove_that_ar_AQC_ar_PBR\"><\/span><strong>14. In figure, AP<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>BQ<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>CR. Prove that ar (AQC) = ar (PBR). <\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 18\" style=\"height: 108px; width: 156px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image033.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABQ and BPQ lie on the same base BQ and between same parallels AP and BQ.<\/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\/Ex9.3\/image007.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABQ) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>BPQ) \u2026\u2026\u2026.(i)<\/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\/Ex9.3\/image001.png\" \/>BQC and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>BQR lie on the same base BQ and between same parallels BQ and CR.<\/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\/Ex9.3\/image007.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>BQC) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>BQR) \u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\">Adding eq (i) and (ii), ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABQ) + ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>BQC) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>BPQ) + ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>BQR)<\/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\/Ex9.3\/image004.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>AQC) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>PBR)<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 9.3<\/p>\n<p style=\"text-align: justify;\"><strong>15. Diagonals AC and BD of a quadrilateral ABCD intersect at O in such a way that ar (AOD) = ar(BOC). Prove that ABCD is a trapezium.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Given that ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>AOD) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>BOC)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 1575\" style=\"height: 94px; width: 180px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image034.png\" \/><\/p>\n<p style=\"text-align: justify;\">Adding <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>AOB both 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\/Ex9.3\/image001.png\" \/>AOD) + ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>AOB) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>BOC) + ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>AOB)<\/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\/Ex9.3\/image004.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABD) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABC)<\/p>\n<p style=\"text-align: justify;\">Since if two triangles equal in area, lie on the same base then, they lie between same parallels. We have <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABD and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ABC lie on common base AB and are equal in 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\/Ex9.3\/image007.png\" \/> They lie in same parallels AB and DC.<\/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\/Ex9.3\/image004.png\" \/> AB<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>DC<\/p>\n<p style=\"text-align: justify;\">Now in quadrilateral ABCD, we have AB<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>DC<\/p>\n<p style=\"text-align: justify;\">Therefore, ABCD is trapezium. [<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image003.png\" \/> In trapezium one pair of opposite sides is parallel]\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 9.3<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"16_In_figure_ar_DRC_ar_DPC_and_ar_BDP_ar_ARC_Show_that_both_the_quadrilaterals_ABCD_and_DCPR_are_trapeziums\"><\/span><strong>16. In figure, ar (DRC) = ar (DPC) and ar (BDP) = ar (ARC). Show that both the quadrilaterals ABCD and DCPR are trapeziums. <\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 17\" style=\"height: 118px; width: 171px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image035.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Given that <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>DRC and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>DPC lie on the same base DC and ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>DPC) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>DRC) \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\/Ex9.3\/image007.png\" \/> DC<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>RP<\/p>\n<p style=\"text-align: justify;\">[If two triangles equal in area, lie on the same base then, they lie between same parallels]\n<p style=\"text-align: justify;\">Therefore, DCPR is trapezium. [<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image003.png\" \/> In trapezium one pair of opposite sides is parallel]\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\/Ex9.3\/image001.png\" \/>BDP) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ARC) \u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\">Subtracting eq. (i) from (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\/Ex9.3\/image001.png\" \/>BDP) \u2013 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>DPC) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ARC) \u2013 ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>DRC)<\/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\/Ex9.3\/image004.png\" \/> ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>BDC) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image001.png\" \/>ADC)<\/p>\n<p style=\"text-align: justify;\">Therefore, AB<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.3\/image020.png\" \/>DC [If two triangles equal in area, lie on the same base then, they lie between same parallels]\n<p style=\"text-align: justify;\">Therefore, ABCD is trapezium<strong>.<\/strong><\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_9_Maths_Exercise_93\"><\/span>NCERT Solutions for Class 9 Maths Exercise 9.3<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>NCERT Solutions for Class 9 Maths 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 9.3 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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