{"id":4999,"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-9-2\/"},"modified":"2018-06-18T15:48:01","modified_gmt":"2018-06-18T10:18:01","slug":"ncert-solutions-for-class-9-maths-exercise-9-2","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-9-2\/","title":{"rendered":"NCERT Solutions for Class 9 Maths Exercise 9.2"},"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-9-2\/#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-9-2\/#1_In_figure_ABCD_is_a_parallelogram_AE_DC_and_CF_AD_If_AB_16_cm_AE_8_cm_and_CF_10_cm_find_AD\" >1. In figure, ABCD is a parallelogram. AE  DC and CF  AD. If AB = 16 cm, AE = 8 cm and CF = 10 cm, find AD.<\/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-9-2\/#2_If_E_F_G_and_H_are_respectively_the_mid-points_of_the_sides_of_a_parallelogram_ABCD_show_that_ar_EFGH_ar_ABCD\" >2. If E, F, G and H are respectively the mid-points of the sides of a parallelogram ABCD, show that ar (EFGH) = ar (ABCD).<\/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-9-2\/#3_P_and_Q_are_any_two_points_lying_on_the_sides_DC_and_AD_respectively_of_a_parallelogram_ABCD_Show_that_ar_APB_ar_BQC\" >3. P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD. Show that ar (APB) = ar (BQC).<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-9-2\/#4_In_figure_P_is_a_point_in_the_interior_of_a_parallelogram_ABCD\" >4. In figure, P is a point in the interior of a parallelogram ABCD.<\/a><ul class='ez-toc-list-level-6' ><li class='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-9-2\/#Adding_eq_i_and_ii\" >Adding eq. (i) and (ii),<\/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-9-2\/#5_In_figure_PQRS_and_ABRS_are_parallelograms_and_X_is_any_point_on_the_side_BR_Show_that\" >5. In figure, PQRS and ABRS are parallelograms and X is any point on the side BR. Show that:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-9-2\/#6_a_farmer_was_having_a_field_in_the_form_of_a_parallelogram_PQRS_She_took_any_point_A_on_RS_and_joined_it_to_points_P_and_Q_In_how_many_parts_the_field_is_divided_What_are_the_shapes_of_these_parts_The_farmer_wants_to_sow_wheat_and_pulses_in_equal_portions_of_the_field_separately_How_should_she_do_it\" >6. a farmer was having a field in the form of a parallelogram PQRS. She took any point A on RS and joined it to points P and Q. In how many parts the field is divided? What are the shapes of these parts? The farmer wants to sow wheat and pulses in equal portions of the field separately. How should she do it?<\/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-9-2\/#So_if_farmer_sows_wheat_in_triangular_shaped_field_APQ_then_she_will_definitely_sow_pulses_in_other_two_triangular_parts_PAS_and_AQR\" >So if farmer sows wheat in triangular shaped field APQ then she will definitely sow pulses in other two triangular parts PAS and AQR.<\/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-10\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-9-2\/#NCERT_Solutions_for_Class_9_Maths_Exercise_92\" >NCERT Solutions for Class 9 Maths Exercise 9.2<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-9-2\/#CBSE_app_for_Class_9\" >CBSE app for Class 9<\/a><\/li><\/ul><\/nav><\/div>\n<p>NCERT Solutions for Class 9 Maths Exercise 9.2 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 9.2\" width=\"170\" height=\"219\" \/><\/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_ABCD_is_a_parallelogram_AE_DC_and_CF_AD_If_AB_16_cm_AE_8_cm_and_CF_10_cm_find_AD\"><\/span><strong>1. In figure, ABCD is a parallelogram. AE <img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image001.png\" \/> DC and CF <img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image001.png\" \/> AD. If AB = 16 cm, AE = 8 cm and CF = 10 cm, find AD. <\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 1528\" style=\"height: 129px; width: 211px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image002.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>ABCD 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\/Ex9.2\/image003.png\" \/>DC = AB <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image004.png\" \/>DC = 16 cm<\/p>\n<p style=\"text-align: justify;\">AE <img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image001.png\" \/> DC [Given]\n<p style=\"text-align: justify;\">Now Area of parallelogram ABCD = Base x Corresponding height<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 22px; width: 192px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image005.png\" \/><\/p>\n<p style=\"text-align: justify;\">Using base AD and height CF, we can find,<\/p>\n<p style=\"text-align: justify;\">Area of parallelogram <img decoding=\"async\" style=\"height: 19px; width: 77px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image006.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image004.png\" \/>128 <img decoding=\"async\" style=\"height: 19px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image007.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image004.png\" \/> AD = <img decoding=\"async\" style=\"height: 41px; width: 29px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image008.png\" \/> = 12.8 cm<\/p>\n<hr \/>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"2_If_E_F_G_and_H_are_respectively_the_mid-points_of_the_sides_of_a_parallelogram_ABCD_show_that_ar_EFGH_ar_ABCD\"><\/span><strong>2. If E, F, G and H are respectively the mid-points of the sides of a parallelogram ABCD, show that ar (EFGH) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image009.png\" \/>ar (ABCD).<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. Given<\/strong>: A parallelogram ABCD. E, F, G and H are mid-points of AB, BC, CD and DA respectively.<\/p>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 1534\" style=\"height: 122px; width: 174px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image010.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>To prove<\/strong>: ar (EFGH) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image009.png\" \/> ar (ABCD)<\/p>\n<p style=\"text-align: justify;\"><strong>Construction<\/strong>: Join HF<\/p>\n<p style=\"text-align: justify;\"><strong>Proof<\/strong>: ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>GHF) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image009.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image012.png\" \/>gm HFCD) \u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\">And ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>HEF) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image009.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image012.png\" \/>gm HABF) \u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\">[If a triangle and a parallelogram are on the same base and between the same parallel then the area of triangle is half of area of parallelogram]\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\/Ex9.2\/image011.png\" \/>GHF) + ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>HEF)<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image009.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image012.png\" \/>gm HFCD) + <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image009.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image012.png\" \/>gm HABF)<\/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\/Ex9.2\/image004.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image012.png\" \/>gm HEFG) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image009.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image012.png\" \/>gm ABCD)<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 9.2<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"3_P_and_Q_are_any_two_points_lying_on_the_sides_DC_and_AD_respectively_of_a_parallelogram_ABCD_Show_that_ar_APB_ar_BQC\"><\/span><strong>3. P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD. Show that ar (APB) = ar (BQC).<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. Given<\/strong>: ABCD is a parallelogram. P is a point on DC and Q is a point on AD.<\/p>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 1531\" style=\"height: 113px; width: 191px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image013.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\/Ex9.2\/image011.png\" \/>APB) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>BQC)<\/p>\n<p style=\"text-align: justify;\"><strong>Construction<\/strong>: Draw PM <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image012.png\" \/> BC and QN <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image012.png\" \/> DC.<\/p>\n<p style=\"text-align: justify;\"><strong>Proof<\/strong>: Since QC is the diagonal of parallelogram QNCD.<\/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\/Ex9.2\/image003.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>QNC) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image009.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image012.png\" \/>gm QNCD) \u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\">Again BQ is the diagonal of parallelogram ABNQ.<\/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\/Ex9.2\/image003.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>BQN) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image009.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image012.png\" \/>gm ABNQ) \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\/Ex9.2\/image011.png\" \/>QNC) + ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>BQN)<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image009.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image012.png\" \/>gm QNCD) + <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image009.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image012.png\" \/>gm ABNQ)<\/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\/Ex9.2\/image004.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>BQC) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image009.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image012.png\" \/>gm ABCD) \u2026\u2026\u2026..(iii)<\/p>\n<p style=\"text-align: justify;\">Again AP is the diagonal of <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image012.png\" \/>gm AMPD.<\/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\/Ex9.2\/image003.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>APM) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image009.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image012.png\" \/>gm AMPD) \u2026\u2026\u2026.(iv)<\/p>\n<p style=\"text-align: justify;\">And PB is the diagonal of <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image012.png\" \/>gm PCBM.<\/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\/Ex9.2\/image003.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>PBM) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image009.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image012.png\" \/>gm PCBM) \u2026\u2026\u2026.(v)<\/p>\n<p style=\"text-align: justify;\">Adding eq. (iv) and (v),<\/p>\n<p style=\"text-align: justify;\">ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>APM) + ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>PBM)<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image009.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image012.png\" \/>gm AMPD) + <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image009.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image012.png\" \/>gm PCBM)<\/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\/Ex9.2\/image004.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>APB) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image009.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image012.png\" \/>gm ABCD) \u2026\u2026\u2026.(vi)<\/p>\n<p style=\"text-align: justify;\">From eq. (iii) and (vi),<\/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\/Ex9.2\/image011.png\" \/>BQC) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>APB) or ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>APB) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>BQC)<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 9.2<\/p>\n<h5 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"4_In_figure_P_is_a_point_in_the_interior_of_a_parallelogram_ABCD\"><\/span><strong>4. In figure, P is a point in the interior of a parallelogram ABCD. <\/strong><span class=\"ez-toc-section-end\"><\/span><\/h5>\n<p style=\"text-align: justify;\"><strong>Show that: <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 14\" style=\"height: 117px; width: 202px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image014.png\" \/> <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(i) ar (APB) + ar (PCD) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image009.png\" \/>ar (ABCD) <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) ar (APD) + ar (PBC) = ar (APB) + ar (PCD) <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i)<\/strong> Draw a line passing through point P and parallel to AB which intersects AD at Q and BC at R respectively.<\/p>\n<p style=\"text-align: justify;\">Now <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>APB and parallelogram ABRQ are on the same base AB and between same parallels AB and QR.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 15\" style=\"height: 111px; width: 169px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image015.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\/Ex9.2\/image003.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>APB) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image009.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image012.png\" \/>gm ABRQ) \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\/Ex9.2\/image011.png\" \/>PCD and parallelogram DCRQ are on the same base AB and between same parallels AB and QR.<\/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\/Ex9.2\/image003.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>PCD) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image009.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image012.png\" \/>gm DCRQ) \u2026\u2026\u2026.(ii)<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Adding_eq_i_and_ii\"><\/span>Adding eq. (i) and (ii),<span class=\"ez-toc-section-end\"><\/span><\/h6>\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\/Ex9.2\/image011.png\" \/>APB) + ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>PCD)<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image009.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image012.png\" \/>gm ABRQ) + <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image009.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image012.png\" \/>gm DCRQ)<\/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\/Ex9.2\/image004.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>APB) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image009.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image012.png\" \/>gm ABCD) \u2026\u2026\u2026.(iii)<\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> Draw a line through P and parallel to AD which intersects AB at M and DC at N. Now <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>APD and parallelogram AMND are on the same base AD and between same parallels AD and MN.<\/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\/Ex9.2\/image003.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>APD) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image009.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image012.png\" \/>gm AMND) \u2026\u2026\u2026.(iv)<\/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\/Ex9.2\/image011.png\" \/>PBC and parallelogram MNCB are on the same base BC and between same parallels BC and MN.<\/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\/Ex9.2\/image003.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>PBC) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image009.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image012.png\" \/>gm MNCB) \u2026\u2026\u2026.(v)<\/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\/Ex9.2\/image011.png\" \/>APD) + ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>PBC)<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image009.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image012.png\" \/>gm AMND) + <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image009.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image012.png\" \/>gm MNCB)<\/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\/Ex9.2\/image004.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>APD) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image009.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image012.png\" \/>gm ABCD) \u2026\u2026\u2026.(vi)<\/p>\n<p style=\"text-align: justify;\">From eq. (iii) and (vi), we get,<\/p>\n<p style=\"text-align: justify;\">ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>APB) + ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>PCD) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>APD) + ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>PBC)<\/p>\n<p style=\"text-align: justify;\">or ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>APD) + ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>PBC) = ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>APB) + ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>PCD)<\/p>\n<p style=\"text-align: justify;\">Hence proved.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 9.2<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"5_In_figure_PQRS_and_ABRS_are_parallelograms_and_X_is_any_point_on_the_side_BR_Show_that\"><\/span><strong>5. In figure, PQRS and ABRS are parallelograms and X is any point on the side BR. Show that:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 146px; width: 202px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image016.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(i) ar (PQRS) = ar (ABRS)<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) ar (AXS) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image009.png\" \/>ar (PQRS)<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i)<\/strong> Parallelogram PQRS and ABRS are on the same base SR and between the same parallels SR and PB.<\/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\/Ex9.2\/image003.png\" \/>ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image012.png\" \/>gm PQRS) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image009.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image012.png\" \/>gm ABRS) \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\/Ex9.2\/image017.png\" \/> parallelograms on the same base and between the same parallels are equal<\/p>\n<p style=\"text-align: justify;\">in area]\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>AXS and <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image012.png\" \/>gm ABRS are on the same base AS and between the same parallels AS and BR.<\/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\/Ex9.2\/image003.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>AXS) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image009.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image012.png\" \/>gm ABRS) \u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\">Using 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\/Ex9.2\/image011.png\" \/>AXS) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image009.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image012.png\" \/>gm PQRS)<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 9.2<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"6_a_farmer_was_having_a_field_in_the_form_of_a_parallelogram_PQRS_She_took_any_point_A_on_RS_and_joined_it_to_points_P_and_Q_In_how_many_parts_the_field_is_divided_What_are_the_shapes_of_these_parts_The_farmer_wants_to_sow_wheat_and_pulses_in_equal_portions_of_the_field_separately_How_should_she_do_it\"><\/span><strong>6. a farmer was having a field in the form of a parallelogram PQRS. She took any point A on RS and joined it to points P and Q. In how many parts the field is divided? What are the shapes of these parts? The farmer wants to sow wheat and pulses in equal portions of the field separately. How should she do it?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>When A is joined with P and Q; the field is divided into three parts viz. <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>PAS, <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>APQ and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>AQR.<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>APQ and parallelogram PQRS are on the same base PQ and between same parallels PQ and SR.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 1540\" style=\"height: 126px; width: 227px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image018.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\/Ex9.2\/image003.png\" \/>ar (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image011.png\" \/>APQ) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image009.png\" \/> ar (<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image012.png\" \/>gm PQRS)<\/p>\n<p style=\"text-align: justify;\">It implies that triangular region APQ covers half portion of parallelogram shaped field PQRS.<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"So_if_farmer_sows_wheat_in_triangular_shaped_field_APQ_then_she_will_definitely_sow_pulses_in_other_two_triangular_parts_PAS_and_AQR\"><\/span>So if farmer sows wheat in triangular shaped field APQ then she will definitely sow pulses in other two triangular parts PAS and AQR.<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: center;\"><strong>Or<\/strong><\/p>\n<p style=\"text-align: justify;\">When she sows pulses in triangular shaped field APQ then she will sow wheat in other two triangular parts PAS and AQR.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 1543\" style=\"height: 104px; width: 183px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch09\/Ex9.2\/image019.jpg\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_9_Maths_Exercise_92\"><\/span>NCERT Solutions for Class 9 Maths Exercise 9.2<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 9.2 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 &#8230; <a title=\"NCERT Solutions for Class 9 Maths Exercise 9.2\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-9-2\/\" aria-label=\"More on NCERT Solutions for Class 9 Maths Exercise 9.2\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":-1,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1376,281],"tags":[283,1344,321,1485,216],"class_list":["post-4999","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics-cbse-class-09","category-ncert-solutions","tag-cbse-study-material","tag-class-9","tag-mathematics","tag-maths","tag-ncert-solutions"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>NCERT Solutions for Class 9 Maths Exercise 9.2 | myCBSEguide<\/title>\n<meta name=\"description\" content=\"NCERT Solutions for Class 9 Maths Exercise 9.2 in PDF format for free download. 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