{"id":5033,"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-8-2\/"},"modified":"2018-06-18T15:01:39","modified_gmt":"2018-06-18T09:31:39","slug":"ncert-solutions-for-class-9-maths-exercise-8-2","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-8-2\/","title":{"rendered":"NCERT Solutions for Class 9 Maths Exercise 8.2"},"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-8-2\/#NCERT_Solutions_for_Class_9_Mathematics_Quadrilaterals\" >NCERT Solutions for Class 9 Mathematics Quadrilaterals<\/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-8-2\/#1_ABCD_is_a_quadrilateral_in_which_P_Q_R_and_S_are_the_mid-points_of_sides_AB_BC_CD_and_DA_respectively_See_figure_AC_is_a_diagonal_Show_that\" >1. ABCD is a quadrilateral in which P, Q, R and S are the mid-points of sides AB, BC, CD and DA respectively (See figure). AC is a diagonal. Show that:<\/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-8-2\/#2_ABCD_is_a_rhombus_and_P_Q_R_S_are_mid-points_of_AB_BC_CD_and_DA_respectively_Prove_that_quadrilateral_PQRS_is_a_rectangle\" >2. ABCD is a rhombus and P, Q, R, S are mid-points of AB, BC, CD and DA respectively. Prove that quadrilateral PQRS is a rectangle.<\/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-8-2\/#3_ABCD_is_a_rectangle_and_P_Q_R_and_S_are_the_mid-points_of_the_sides_AB_BC_CD_and_DA_respectively_Show_that_the_quadrilateral_PQRS_is_a_rhombus\" >3. ABCD is a rectangle and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.<\/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-8-2\/#4_ABCD_is_a_trapezium_in_which_AB_DC_BD_is_a_diagonal_and_E_is_the_mid-point_of_AD_A_line_is_drawn_through_E_parallel_to_AB_intersecting_BC_at_F_See_figure_Show_that_F_is_the_mid-point_of_BC\" >4. ABCD is a trapezium, in which AB  DC, BD is a diagonal and E is the mid-point of AD. A line is drawn through E, parallel to AB intersecting BC at F (See figure). Show that F 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-6\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-8-2\/#5_In_a_parallelogram_ABCD_E_and_F_are_the_mid-points_of_sides_AB_and_CD_respectively_See_figure_Show_that_the_line_segments_AF_and_EC_trisect_the_diagonal_BD\" >5. In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively (See figure). Show that the line segments AF and EC trisect the diagonal BD.<\/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-8-2\/#Since_the_segment_drawn_through_the_mid-point_of_one_side_of_a_triangle_and_parallel_to_the_other_side_bisects_the_third_side\" >Since the segment drawn through the mid-point of one side of a triangle and parallel to the other side bisects the third side.<\/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-8-2\/#6_Show_that_the_line_segments_joining_the_mid-points_of_opposite_sides_of_a_quadrilateral_bisect_each_other\" >6. Show that the line segments joining the mid-points of opposite sides of a quadrilateral bisect each other.<\/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-8-2\/#7_ABC_is_a_triangle_right_angled_at_C_A_line_through_the_mid-point_M_of_hypotenuse_AB_and_parallel_to_BC_intersects_AC_at_D\" >7. ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D.<\/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-8-2\/#iii_In_AMD_and_CMD\" >(iii) In AMD and CMD,<\/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-11\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-8-2\/#NCERT_Solutions_for_Class_9_Maths_Exercise_82\" >NCERT Solutions for Class 9 Maths Exercise 8.2<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-8-2\/#CBSE_app_for_Class_9\" >CBSE app for Class 9<\/a><\/li><\/ul><\/nav><\/div>\n<p>NCERT Solutions for Class 9 Maths Exercise 8.2 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>Quadrilateral<\/strong><strong>\u00a0<\/strong><strong><a class=\"button\" href=\"https:\/\/mycbseguide.com\/downloads\/cbse-class-09-mathematics-quadrilaterals\/1242\/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 8.2\" width=\"161\" height=\"208\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_9_Mathematics_Quadrilaterals\"><\/span>NCERT Solutions for Class 9 Mathematics Quadrilaterals<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"1_ABCD_is_a_quadrilateral_in_which_P_Q_R_and_S_are_the_mid-points_of_sides_AB_BC_CD_and_DA_respectively_See_figure_AC_is_a_diagonal_Show_that\"><\/span><strong>1. ABCD is a quadrilateral in which P, Q, R and S are the mid-points of sides AB, BC, CD and DA respectively (See figure). AC is a diagonal. Show that:<u> <\/u><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong><u><img decoding=\"async\" id=\"Picture 2020\" style=\"height: 154px; width: 162px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image001.jpg\" \/><\/u><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(i) SR <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image002.png\" \/> AC and SR = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image003.png\" \/> AC<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) PQ = SR<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) PQRS is a parallelogram.<\/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\/ch08\/Ex8.2\/image004.png\" \/> ABC, P is the mid-point of AB and Q is the mid-point of BC.<\/p>\n<p style=\"text-align: justify;\">Then PQ <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image002.png\" \/> AC and PQ = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image003.png\" \/> AC<\/p>\n<p style=\"text-align: justify;\"><strong>(i)<\/strong> In <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image004.png\" \/> ACD, R is the mid-point of CD and S is the mid-point of AD.<\/p>\n<p style=\"text-align: justify;\">Then SR <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image002.png\" \/> AC and SR = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image003.png\" \/> AC<\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> Since PQ = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image003.png\" \/> AC and SR = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image003.png\" \/> AC<\/p>\n<p style=\"text-align: justify;\">Therefore, PQ = SR<\/p>\n<p style=\"text-align: justify;\"><strong>(iii)<\/strong> Since PQ <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image002.png\" \/> AC and SR <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image002.png\" \/> AC<\/p>\n<p style=\"text-align: justify;\">Therefore, PQ <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image002.png\" \/> SR [two lines parallel to given line are parallel to each other]\n<p style=\"text-align: justify;\">Now PQ = SR and PQ <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image002.png\" \/> SR<\/p>\n<p style=\"text-align: justify;\">Therefore, PQRS is a parallelogram.<\/p>\n<hr \/>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"2_ABCD_is_a_rhombus_and_P_Q_R_S_are_mid-points_of_AB_BC_CD_and_DA_respectively_Prove_that_quadrilateral_PQRS_is_a_rectangle\"><\/span><strong>2. ABCD is a rhombus and P, Q, R, S are mid-points of AB, BC, CD and DA respectively. Prove that quadrilateral PQRS is a rectangle.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. Given<\/strong>: P, Q, R and S are the mid-points of respective sides AB, BC, CD and DA of rhombus. PQ, QR, RS and SP are joined.<\/p>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 2023\" style=\"height: 194px; width: 183px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image005.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>To prove<\/strong>: PQRS is a rectangle.<\/p>\n<p style=\"text-align: justify;\"><strong>Construction<\/strong>: Join A and C.<\/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\/ch08\/Ex8.2\/image004.png\" \/>ABC, P is the mid-point of AB and Q 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\/ch08\/Ex8.2\/image006.png\" \/>PQ <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image002.png\" \/> AC and PQ = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image003.png\" \/> AC \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\/ch08\/Ex8.2\/image004.png\" \/>ADC, R is the mid-point of CD and S is the mid-point of AD.<\/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\/ch08\/Ex8.2\/image006.png\" \/>SR <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image002.png\" \/> AC and SR = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image003.png\" \/> AC \u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\">From eq. (i) and (ii), PQ <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image002.png\" \/> SR and PQ = SR<\/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\/ch08\/Ex8.2\/image006.png\" \/>PQRS is a parallelogram.<\/p>\n<p style=\"text-align: justify;\">Now ABCD is a rhombus. [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\/ch08\/Ex8.2\/image006.png\" \/>AB = BC<\/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\/ch08\/Ex8.2\/image007.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image003.png\" \/> AB = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image003.png\" \/> BC <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image007.png\" \/> PB = 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\/ch08\/Ex8.2\/image006.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image008.png\" \/>1 = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image008.png\" \/>2 [Angles opposite to equal sides are equal]\n<p style=\"text-align: justify;\">Now in triangles APS and CQR, we have,<\/p>\n<p style=\"text-align: justify;\">AP = CQ [P and Q are the mid-points of AB and BC and AB = BC]\n<p style=\"text-align: justify;\">Similarly, AS = CR and PS = QR [Opposite sides of a parallelogram]\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\/ch08\/Ex8.2\/image006.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image004.png\" \/>APS <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image009.png\" \/>CQR [By SSS congreuancy]\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\/ch08\/Ex8.2\/image007.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image008.png\" \/>3 = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image008.png\" \/>4 [By C.P.C.T.]\n<p style=\"text-align: justify;\">Now we have <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image008.png\" \/>1 + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image008.png\" \/>SPQ + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image008.png\" \/>3 = <img decoding=\"async\" style=\"height: 19px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image010.png\" \/><\/p>\n<p style=\"text-align: justify;\">And <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image008.png\" \/>2 + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image008.png\" \/>PQR + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image008.png\" \/>4 = <img decoding=\"async\" style=\"height: 19px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image010.png\" \/> [Linear pairs]\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\/ch08\/Ex8.2\/image006.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image008.png\" \/>1 + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image008.png\" \/>SPQ + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image008.png\" \/>3 = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image008.png\" \/>2 + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image008.png\" \/>PQR + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image008.png\" \/>4<\/p>\n<p style=\"text-align: justify;\">Since <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image008.png\" \/>1 = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image008.png\" \/>2 and <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image008.png\" \/>3 = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image008.png\" \/>4 [Proved above]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image006.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image008.png\" \/>SPQ = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image008.png\" \/>PQR \u2026\u2026\u2026.(iii)<\/p>\n<p style=\"text-align: justify;\">Now PQRS is a parallelogram [Proved above]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image006.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image008.png\" \/>SPQ + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image008.png\" \/>PQR = <img decoding=\"async\" style=\"height: 19px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image010.png\" \/>\u2026\u2026\u2026.(iv) [Interior angles]\n<p style=\"text-align: justify;\">Using eq. (iii) and (iv),<\/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\/ch08\/Ex8.2\/image008.png\" \/>SPQ + <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image008.png\" \/>SPQ = <img decoding=\"async\" style=\"height: 19px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image010.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image007.png\" \/>2<img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image008.png\" \/>SPQ = <img decoding=\"async\" style=\"height: 19px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image010.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\/ch08\/Ex8.2\/image007.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image008.png\" \/>SPQ = <img decoding=\"async\" style=\"height: 19px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image011.png\" \/><\/p>\n<p style=\"text-align: justify;\">Hence PQRS is a rectangle.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 8.2<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"3_ABCD_is_a_rectangle_and_P_Q_R_and_S_are_the_mid-points_of_the_sides_AB_BC_CD_and_DA_respectively_Show_that_the_quadrilateral_PQRS_is_a_rhombus\"><\/span><strong>3. ABCD is a rectangle and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. Given<\/strong>: A rectangle ABCD in which P, Q, R and S are the mid-points of the sides AB, BC, CD and DA respectively. PQ, QR, RS and SP are joined.<\/p>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 2026\" style=\"height: 157px; width: 229px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image012.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>To prove<\/strong>: PQRS is a rhombus.<\/p>\n<p style=\"text-align: justify;\"><strong>Construction<\/strong>: Join AC.<\/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\/ch08\/Ex8.2\/image004.png\" \/>ABC, P and Q are the mid-points of sides AB, BC respectively.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image006.png\" \/>PQ <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image002.png\" \/> AC and PQ = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image003.png\" \/> AC \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\/ch08\/Ex8.2\/image004.png\" \/>ADC, R and S are the mid-points of sides CD, AD respectively.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image006.png\" \/>SR <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image002.png\" \/> AC and SR = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image003.png\" \/> AC \u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\">From eq. (i) and (ii), PQ <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image002.png\" \/> SR and PQ = SR \u2026\u2026\u2026.(iii)<\/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\/ch08\/Ex8.2\/image006.png\" \/>PQRS is a parallelogram.<\/p>\n<p style=\"text-align: justify;\">Now ABCD is a rectangle. [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\/ch08\/Ex8.2\/image006.png\" \/>AD = BC<\/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\/ch08\/Ex8.2\/image007.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image003.png\" \/>AD = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image003.png\" \/>BC <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image007.png\" \/> AS = BQ \u2026\u2026\u2026.(iv)<\/p>\n<p style=\"text-align: justify;\">In triangles APS and BPQ,<\/p>\n<p style=\"text-align: justify;\">AP = BP [P is the mid-point of AB]\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\/ch08\/Ex8.2\/image008.png\" \/>PAS = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image008.png\" \/>PBQ [Each <img decoding=\"async\" style=\"height: 19px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image011.png\" \/> ]\n<p style=\"text-align: justify;\">And AS = BQ [From eq. (iv)]\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\/ch08\/Ex8.2\/image006.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image004.png\" \/> APS <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image009.png\" \/>BPQ [By SAS 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\/ch08\/Ex8.2\/image007.png\" \/>PS = PQ [By C.P.C.T.] \u2026\u2026\u2026(v)<\/p>\n<p style=\"text-align: justify;\">From eq. (iii) and (v), we get that PQRS is a parallelogram.<\/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\/ch08\/Ex8.2\/image007.png\" \/>PS = PQ<\/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\/ch08\/Ex8.2\/image007.png\" \/>Two adjacent sides are equal.<\/p>\n<p style=\"text-align: justify;\">Hence, PQRS is a rhombus.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 8.2<\/p>\n<h6><span class=\"ez-toc-section\" id=\"4_ABCD_is_a_trapezium_in_which_AB_DC_BD_is_a_diagonal_and_E_is_the_mid-point_of_AD_A_line_is_drawn_through_E_parallel_to_AB_intersecting_BC_at_F_See_figure_Show_that_F_is_the_mid-point_of_BC\"><\/span><strong>4. ABCD is a trapezium, in which AB <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image002.png\" \/> DC, BD is a diagonal and E is the mid-point of AD. A line is drawn through E, parallel to AB intersecting BC at F (See figure). Show that F is the mid-point of BC.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 6\" style=\"height: 125px; width: 202px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image013.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let diagonal BD intersect line EF at point P.<\/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\/ch08\/Ex8.2\/image004.png\" \/>DAB,<\/p>\n<p style=\"text-align: justify;\">E is the mid-point of AD and EP <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image002.png\" \/> AB [<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image014.png\" \/> EF <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image002.png\" \/> AB (given) P is the part of EF]\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\/ch08\/Ex8.2\/image006.png\" \/>P is the mid-point of other side, BD of <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image004.png\" \/>DAB.<\/p>\n<p style=\"text-align: justify;\">[A line drawn through the mid-point of one side of a triangle, parallel to another side intersects the third side at the mid-point]\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\/ch08\/Ex8.2\/image004.png\" \/>BCD,<\/p>\n<p style=\"text-align: justify;\">P is the mid-point of BD and PF <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image002.png\" \/> DC [<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image014.png\" \/> EF <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image002.png\" \/> AB (given) and AB <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image002.png\" \/> DC (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\/ch08\/Ex8.2\/image006.png\" \/> EF <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image002.png\" \/> DC and PF is a part of 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\/ch08\/Ex8.2\/image006.png\" \/> F is the mid-point of other side, BC of <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image004.png\" \/>BCD. [Converse of mid-point of theorem]\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 8.2<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"5_In_a_parallelogram_ABCD_E_and_F_are_the_mid-points_of_sides_AB_and_CD_respectively_See_figure_Show_that_the_line_segments_AF_and_EC_trisect_the_diagonal_BD\"><\/span><strong>5. In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively (See figure). Show that the line segments AF and EC trisect the diagonal BD. <\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 2032\" style=\"height: 156px; width: 166px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image015.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Since E and F are the mid-points of AB and CD respectively.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image006.png\" \/>AE = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image003.png\" \/> AB and CF = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image003.png\" \/> CD\u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\">But 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\/ch08\/Ex8.2\/image006.png\" \/>AB = CD and AB <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image002.png\" \/> 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\/ch08\/Ex8.2\/image007.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image003.png\" \/> AB = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image003.png\" \/> CD and AB <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image002.png\" \/> 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\/ch08\/Ex8.2\/image007.png\" \/> AE = FC and AE <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image002.png\" \/> FC [From eq. (i)]\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\/ch08\/Ex8.2\/image006.png\" \/>AECF is a parallelogram.<\/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\/ch08\/Ex8.2\/image007.png\" \/>FA <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image002.png\" \/> CE <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image007.png\" \/>FP <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image002.png\" \/> CQ [FP is a part of FA and CQ is a part of CE] \u2026\u2026&#8230;(ii)<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Since_the_segment_drawn_through_the_mid-point_of_one_side_of_a_triangle_and_parallel_to_the_other_side_bisects_the_third_side\"><\/span>Since the segment drawn through the mid-point of one side of a triangle and parallel to the other side bisects the third side.<span class=\"ez-toc-section-end\"><\/span><\/h6>\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\/ch08\/Ex8.2\/image004.png\" \/>DCQ, F is the mid-point of CD and <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image007.png\" \/>FP <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image002.png\" \/> CQ<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image006.png\" \/> P is the mid-point of DQ.<\/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\/ch08\/Ex8.2\/image007.png\" \/> DP = PQ \u2026\u2026\u2026.(iii)<\/p>\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\/ch08\/Ex8.2\/image004.png\" \/>ABP, E is the mid-point of AB and <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image007.png\" \/>EQ <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image002.png\" \/> AP<\/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\/ch08\/Ex8.2\/image006.png\" \/> Q is the mid-point of BP.<\/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\/ch08\/Ex8.2\/image007.png\" \/> BQ = PQ \u2026\u2026\u2026.(iv)<\/p>\n<p style=\"text-align: justify;\">From eq. (iii) and (iv),<\/p>\n<p style=\"text-align: justify;\">DP = PQ = BQ \u2026\u2026\u2026(v)<\/p>\n<p style=\"text-align: justify;\">Now BD = BQ + PQ + DP = BQ + BQ + BQ = 3BQ<\/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\/ch08\/Ex8.2\/image007.png\" \/>BQ = <img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image016.png\" \/> BD \u2026\u2026\u2026.(vi)<\/p>\n<p style=\"text-align: justify;\">From eq. (v) and (vi),<\/p>\n<p style=\"text-align: justify;\">DP = PQ = BQ = <img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image016.png\" \/> BD<\/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\/ch08\/Ex8.2\/image007.png\" \/>Points P and Q trisects BD.<\/p>\n<p style=\"text-align: justify;\">So AF and CE trisects BD.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 8.2<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"6_Show_that_the_line_segments_joining_the_mid-points_of_opposite_sides_of_a_quadrilateral_bisect_each_other\"><\/span><strong>6. Show that the line segments joining the mid-points of opposite sides of a quadrilateral bisect each other.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. Given<\/strong>: A quadrilateral ABCD in which EG and FH are the line-segments joining the mid-points of opposite sides of a quadrilateral.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 2035\" style=\"height: 156px; width: 207px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image017.jpg\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>To prove<\/strong>: EG and FH bisect each other.<\/p>\n<p style=\"text-align: justify;\"><strong>Construction<\/strong>: Join AC, EF, FG, GH and HE.<\/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\/ch08\/Ex8.2\/image004.png\" \/>ABC, E and F are the mid-points of respective sides AB and 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\/ch08\/Ex8.2\/image006.png\" \/>EF <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image002.png\" \/> AC and EF <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image003.png\" \/> AC \u2026\u2026\u2026.(i)<\/p>\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\/ch08\/Ex8.2\/image004.png\" \/>ADC,<\/p>\n<p style=\"text-align: justify;\">G and H are the mid-points of respective sides CD and AD.<\/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\/ch08\/Ex8.2\/image006.png\" \/>HG <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image002.png\" \/> AC and HG <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image003.png\" \/> AC \u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\">From eq. (i) and (ii),<\/p>\n<p style=\"text-align: justify;\">EF <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image002.png\" \/> HG and EF = HG<\/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\/ch08\/Ex8.2\/image006.png\" \/>EFGH is a parallelogram.<\/p>\n<p style=\"text-align: justify;\">Since the diagonals of a parallelogram bisect each other, therefore line segments (i.e. diagonals) EG and FH (of parallelogram EFGH) bisect each other.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 8.2<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"7_ABC_is_a_triangle_right_angled_at_C_A_line_through_the_mid-point_M_of_hypotenuse_AB_and_parallel_to_BC_intersects_AC_at_D\"><\/span><strong>7. ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. (i)<\/strong> In <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image004.png\" \/>ABC, M is the mid-point of AB [Given]\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 2038\" style=\"height: 167px; width: 183px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image018.jpg\" \/><\/p>\n<p style=\"text-align: justify;\">MD <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image002.png\" \/> BC<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image006.png\" \/>AD = DC [Converse of mid-point theorem]\n<p style=\"text-align: justify;\">Thus D is the mid-point of AC.<\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> <img decoding=\"async\" style=\"height: 21px; width: 19px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image019.png\" \/> BC (given) consider AC as a transversal.<\/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\/ch08\/Ex8.2\/image006.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image008.png\" \/>1 = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image008.png\" \/>C [Corresponding angles]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image007.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image008.png\" \/>1 = <img decoding=\"async\" style=\"height: 19px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image011.png\" \/> [<img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image008.png\" \/>C = <img decoding=\"async\" style=\"height: 19px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image011.png\" \/>]\n<p style=\"text-align: justify;\">Thus MD <img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image020.png\" \/> AC.<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"iii_In_AMD_and_CMD\"><\/span><strong>(iii)<\/strong> In <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image004.png\" \/>AMD and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image004.png\" \/>CMD,<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\">AD = DC [proved above]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image008.png\" \/>1 = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image008.png\" \/>2 = <img decoding=\"async\" style=\"height: 19px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image011.png\" \/> [proved above]\n<p style=\"text-align: justify;\">MD = MD [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\/ch08\/Ex8.2\/image006.png\" \/> <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image004.png\" \/>AMD <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image009.png\" \/>CMD [By SAS 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\/ch08\/Ex8.2\/image007.png\" \/> AM = CM [By C.P.C.T.] \u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\">Given that M 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\/ch08\/Ex8.2\/image006.png\" \/> AM = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image003.png\" \/> AB \u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\">From eq. (i) and (ii),<\/p>\n<p style=\"text-align: justify;\">CM = AM = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch08\/Ex8.2\/image003.png\" \/> AB<\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_9_Maths_Exercise_82\"><\/span>NCERT Solutions for Class 9 Maths Exercise 8.2<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 8.2 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 8.2\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-8-2\/\" aria-label=\"More on NCERT Solutions for Class 9 Maths Exercise 8.2\">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-5033","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 8.2 | myCBSEguide<\/title>\n<meta name=\"description\" content=\"NCERT Solutions for Class 9 Maths Exercise 8.2 in PDF format for free download. 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