{"id":4963,"date":"2016-05-19T09:49:00","date_gmt":"2016-05-19T04:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-10-maths-exercise-6-2\/"},"modified":"2023-03-22T15:17:23","modified_gmt":"2023-03-22T09:47:23","slug":"ncert-solutions-class-10-maths-exercise-6-2","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-10-maths-exercise-6-2\/","title":{"rendered":"NCERT Solutions for Class 10 Maths Exercise 6.2"},"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-class-10-maths-exercise-6-2\/#NCERT_Solutions_for_Class_10_Maths_Triangles\" >NCERT Solutions for Class 10 Maths\u00a0Triangles<\/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-class-10-maths-exercise-6-2\/#1_In_figure_i_and_ii_DE_BC_Find_EC_in_i_and_AD_in_ii\" >1. In figure (i) and (ii), DE  BC. Find EC in (i) and AD in (ii).<\/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-class-10-maths-exercise-6-2\/#2_E_and_F_are_points_on_the_sides_PQ_and_PR_respectively_of_a_PQR_For_each_of_the_following_cases_state_whether_EF_QR\" >2. E and F are points on the sides PQ and PR respectively of a PQR. For each of the following cases, state whether EF  QR:<\/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-class-10-maths-exercise-6-2\/#EF_is_not_parallel_to_QR\" >EF is not parallel to QR.<\/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-class-10-maths-exercise-6-2\/#3_In_figure_if_LM_CB_and_LN_CD_prove_that\" >3. In figure, if LM  CB and LN  CD, prove that<\/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-class-10-maths-exercise-6-2\/#4_In_figure_DE_AC_and_DF_AE_Prove_that\" >4. In figure, DE  AC and DF  AE. Prove that<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-10-maths-exercise-6-2\/#5_In_figure_DE_OQ_and_DF_OR_Show_that_EF_QR\" >5. In figure, DE  OQ and DF  OR. Show that EF  QR.<\/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-class-10-maths-exercise-6-2\/#6_In_figure_A_B_and_C_are_points_on_OP_OQ_and_OR_respectively_such_that_AB_PQ_and_AC_PR_Show_that_BC_QR\" >6. In figure, A, B and C are points on OP, OQ and OR respectively such that AB  PQ and AC  PR. Show that BC  QR.<\/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-class-10-maths-exercise-6-2\/#7_Using_Theorem_61_prove_that_a_line_drawn_through_the_mid-point_of_one_side_of_a_triangle_parallel_to_another_side_bisects_the_third_side_Recall_that_you_have_proved_it_in_Class_IX\" >7. Using Theorem 6.1, prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side. (Recall that you have proved it in Class IX).<\/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-class-10-maths-exercise-6-2\/#8_Using_Theorem_62_prove_that_the_line_joining_the_mid-points_of_any_two_sides_of_a_triangle_is_parallel_to_the_third_side_Recall_that_you_have_done_it_in_Class_IX\" >8. Using Theorem 6.2, prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side. (Recall that you have done it in Class IX).<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-10-maths-exercise-6-2\/#9_ABCD_is_a_trapezium_in_which_AB_DC_and_its_diagonals_intersect_each_other_at_the_point_O_Show_that\" >9. ABCD is a trapezium in which AB  DC and its diagonals intersect each other at the point O. Show that<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-10-maths-exercise-6-2\/#Construction_Through_O_draw_OE_AB_ie_OE_DC\" >Construction: Through O, draw OE  AB, i.e. OE  DC.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-10-maths-exercise-6-2\/#10_The_diagonals_of_a_quadrilateral_ABCD_intersect_each_other_at_the_point_O_such_that_Such_that_ABCD_is_a_trapezium\" >10. The diagonals of a quadrilateral ABCD intersect each other at the point O such that  Such that ABCD is a trapezium.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-10-maths-exercise-6-2\/#Construction_Through_O_draw_OE_AB_meeting_AD_at_E\" >Construction: Through O, draw OE  AB meeting AD at E.<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-10-maths-exercise-6-2\/#NCERT_Solutions_for_Class_10_Maths_Exercise_62\" >NCERT Solutions for Class 10 Maths Exercise 6.2<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-10-maths-exercise-6-2\/#CBSE_app_for_Class_10\" >CBSE app for Class 10<\/a><\/li><\/ul><\/nav><\/div>\n<p>NCERT Solutions for Class 10 Maths Exercise 6.2 Class 10 Maths 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 10 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 Maths Triangles<\/strong><strong>\u00a0<\/strong><strong><a class=\"button\" href=\"https:\/\/mycbseguide.com\/downloads\/cbse-class-10-mathematics-triangles\/1208\/ncert-solutions\/5\/\">Download as PDF<\/a><\/strong><\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_10_Maths_Triangles\"><\/span>NCERT Solutions for Class 10 Maths\u00a0Triangles<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h6><span class=\"ez-toc-section\" id=\"1_In_figure_i_and_ii_DE_BC_Find_EC_in_i_and_AD_in_ii\"><\/span><strong>1. In figure (i) and (ii), DE <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> BC. Find EC in (i) and AD in (ii). <\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p><img decoding=\"async\" style=\"height: 132px; width: 392px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image002.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i)<\/strong> Since DE <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.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\/10\/mathematics\/ch06\/Ex6.2\/image003.png\" \/> <img decoding=\"async\" style=\"height: 41px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image004.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\/10\/mathematics\/ch06\/Ex6.2\/image005.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 64px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/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\/10\/mathematics\/ch06\/Ex6.2\/image005.png\" \/> EC = <img decoding=\"async\" style=\"height: 41px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/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\/10\/mathematics\/ch06\/Ex6.2\/image005.png\" \/> EC = 2 cm<\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong>Since DE <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.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\/10\/mathematics\/ch06\/Ex6.2\/image003.png\" \/> <img decoding=\"async\" style=\"height: 41px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image004.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\/10\/mathematics\/ch06\/Ex6.2\/image005.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image008.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\/10\/mathematics\/ch06\/Ex6.2\/image005.png\" \/> AD = <img decoding=\"async\" style=\"height: 41px; width: 57px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image009.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\/10\/mathematics\/ch06\/Ex6.2\/image005.png\" \/> EC = 2.4 cm<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.2<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"2_E_and_F_are_points_on_the_sides_PQ_and_PR_respectively_of_a_PQR_For_each_of_the_following_cases_state_whether_EF_QR\"><\/span><strong>2. E and F are points on the sides PQ and PR respectively of a <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image010.png\" \/>PQR. For each of the following cases, state whether EF <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> QR:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(i) PE = 3.9 cm, EQ = 4 cm, PF = 3.6 cm and FR = 2.4 cm<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm and PF = 0.36 cm<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i)<\/strong>Given: PE = 3.9 cm, EQ = 4 cm, PF = 3.6 cm and FR = 2.4 cm<\/p>\n<p style=\"text-align: justify;\">Now, <img decoding=\"async\" style=\"height: 44px; width: 67px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image011.png\" \/> = 0.97 cm<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 110px; width: 130px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image012.png\" \/><\/p>\n<p style=\"text-align: justify;\">And <img decoding=\"async\" style=\"height: 41px; width: 67px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image013.png\" \/> = 1.2 cm<\/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\/10\/mathematics\/ch06\/Ex6.2\/image014.png\" \/> <img decoding=\"async\" style=\"height: 44px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image015.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore, EF does not divide the sides PQ and PR of <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image010.png\" \/>PQR in the same ratio.<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"EF_is_not_parallel_to_QR\"><\/span><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image003.png\" \/>EF is not parallel to QR.<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong>Given: PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm<\/p>\n<p style=\"text-align: justify;\">Now, <img decoding=\"async\" style=\"height: 44px; width: 67px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image016.png\" \/> = <img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image017.png\" \/> cm<\/p>\n<p style=\"text-align: justify;\">And <img decoding=\"async\" style=\"height: 41px; width: 53px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image018.png\" \/> cm<\/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\/10\/mathematics\/ch06\/Ex6.2\/image014.png\" \/> <img decoding=\"async\" style=\"height: 44px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image019.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore, EF divides the sides PQ and PR of <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image010.png\" \/>PQR in the same ratio.<\/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\/10\/mathematics\/ch06\/Ex6.2\/image003.png\" \/>EF is parallel to QR.<\/p>\n<p style=\"text-align: justify;\"><strong>(iii)<\/strong>Given: PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm and PF = 0.36 cm<\/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\/10\/mathematics\/ch06\/Ex6.2\/image005.png\" \/> EQ = PQ \u2013 PE = 1.28 \u2013 0.18 = 1.10 cm<\/p>\n<p style=\"text-align: justify;\">And ER = PR \u2013 PF = 2.56 \u2013 0.36 = 2.20 cm<\/p>\n<p style=\"text-align: justify;\">Now, <img decoding=\"async\" style=\"height: 44px; width: 116px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image020.png\" \/> = <img decoding=\"async\" style=\"height: 41px; width: 23px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image021.png\" \/> cm<\/p>\n<p style=\"text-align: justify;\">And <img decoding=\"async\" style=\"height: 41px; width: 117px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image022.png\" \/> = <img decoding=\"async\" style=\"height: 41px; width: 23px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image021.png\" \/>cm<\/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\/10\/mathematics\/ch06\/Ex6.2\/image014.png\" \/> <img decoding=\"async\" style=\"height: 44px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image019.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore, EF divides the sides PQ and PR of <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image010.png\" \/>PQR in the same ratio.<\/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\/10\/mathematics\/ch06\/Ex6.2\/image003.png\" \/>EF is parallel to QR.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.2<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"3_In_figure_if_LM_CB_and_LN_CD_prove_that\"><\/span><strong>3. In figure, if LM <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> CB and LN <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> CD, prove that <img decoding=\"async\" style=\"height: 41px; width: 80px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image023.png\" \/> <\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 101\" style=\"height: 127px; width: 202px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image024.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>In <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image010.png\" \/>ABC, LM <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> CB<\/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\/10\/mathematics\/ch06\/Ex6.2\/image003.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image025.png\" \/>[Basic Proportionality theorem] \u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\">And in <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image010.png\" \/>ACD, LN <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> CD<\/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\/10\/mathematics\/ch06\/Ex6.2\/image003.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image026.png\" \/>[Basic Proportionality theorem] \u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\">From eq. (i) and (ii), we have<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 41px; width: 75px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image027.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.2<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"4_In_figure_DE_AC_and_DF_AE_Prove_that\"><\/span><strong>4. In figure, DE <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> AC and DF <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> AE. Prove that <img decoding=\"async\" style=\"height: 41px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image028.png\" \/> <\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 104\" style=\"height: 113px; width: 159px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image029.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>In <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image010.png\" \/>BCA, DE <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> AC<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image003.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image030.png\" \/>[Basic Proportionality theorem] \u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\">And in <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image010.png\" \/>BEA, DF <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> AE<\/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\/10\/mathematics\/ch06\/Ex6.2\/image003.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image031.png\" \/>[Basic Proportionality theorem] \u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\">From eq. (i) and (ii), we have<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 41px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image032.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.2<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"5_In_figure_DE_OQ_and_DF_OR_Show_that_EF_QR\"><\/span><strong>5. In figure, DE <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> OQ and DF <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> OR. Show that EF <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> QR.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 107\" style=\"height: 128px; width: 187px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image033.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>In <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image010.png\" \/>PQO, DE <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> OQ<\/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\/10\/mathematics\/ch06\/Ex6.2\/image003.png\" \/><img decoding=\"async\" style=\"height: 44px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image034.png\" \/>[Basic Proportionality theorem] \u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\">And in <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image010.png\" \/>POR, DF <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> OR<\/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\/10\/mathematics\/ch06\/Ex6.2\/image003.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image035.png\" \/>[Basic Proportionality theorem] \u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\">From eq. (i) and (ii), we have<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 44px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image019.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image003.png\" \/>EF <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> QR [By the converse of BPT]\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.2<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"6_In_figure_A_B_and_C_are_points_on_OP_OQ_and_OR_respectively_such_that_AB_PQ_and_AC_PR_Show_that_BC_QR\"><\/span><strong>6. In figure, A, B and C are points on OP, OQ and OR respectively such that AB <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> PQ and AC <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> PR. Show that BC <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> QR.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 110\" style=\"height: 149px; width: 207px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image036.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. Given<\/strong>: O is any point in <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image010.png\" \/>PQR, in which AB <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> PQ and AC <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> PR.<\/p>\n<p style=\"text-align: justify;\"><strong>To prove<\/strong>: BC <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> QR<\/p>\n<p style=\"text-align: justify;\"><strong>Construction<\/strong>: Join BC.<\/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\/10\/mathematics\/ch06\/Ex6.2\/image010.png\" \/>OPQ, AB <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> PQ<\/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\/10\/mathematics\/ch06\/Ex6.2\/image003.png\" \/><img decoding=\"async\" style=\"height: 44px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image037.png\" \/>[Basic Proportionality theorem] \u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\">And in <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image010.png\" \/>OPR, AC <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> PR<\/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\/10\/mathematics\/ch06\/Ex6.2\/image003.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image038.png\" \/>[Basic Proportionality theorem] \u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\">From eq. (i) and (ii), we have<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 44px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image039.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image014.png\" \/>In <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image010.png\" \/>OQR, B and C are points dividing the sides OQ and OR in the same ratio.<\/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\/10\/mathematics\/ch06\/Ex6.2\/image003.png\" \/>By the converse of Basic Proportionality theorem,<\/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\/10\/mathematics\/ch06\/Ex6.2\/image005.png\" \/>BC <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> QR<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.2<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"7_Using_Theorem_61_prove_that_a_line_drawn_through_the_mid-point_of_one_side_of_a_triangle_parallel_to_another_side_bisects_the_third_side_Recall_that_you_have_proved_it_in_Class_IX\"><\/span><strong>7. Using Theorem 6.1, prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side. (Recall that you have proved it in Class IX).<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. Given<\/strong>: A triangle ABC, in which D is the mid-point of side AB<\/p>\n<p style=\"text-align: justify;\">and the line DE is drawn parallel to BC, meeting AC at E.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 122px; width: 176px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image040.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>To prove<\/strong>: AE = EC<\/p>\n<p style=\"text-align: justify;\"><strong>Proo<\/strong>f: Since DE <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.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\/10\/mathematics\/ch06\/Ex6.2\/image003.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image004.png\" \/>[Basic Proportionality theorem] \u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\">But AD = DB [Given]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image005.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 52px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image041.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\/10\/mathematics\/ch06\/Ex6.2\/image005.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image042.png\" \/> [From eq. (i)]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image005.png\" \/> AE = EC<\/p>\n<p style=\"text-align: justify;\">Hence, E is the mid-point of the third side AC.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.2<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"8_Using_Theorem_62_prove_that_the_line_joining_the_mid-points_of_any_two_sides_of_a_triangle_is_parallel_to_the_third_side_Recall_that_you_have_done_it_in_Class_IX\"><\/span><strong>8. Using Theorem 6.2, prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side. (Recall that you have done it in Class IX).<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. Given<\/strong>: A triangle ABC, in which D and E are the mid-points of<\/p>\n<p style=\"text-align: justify;\">sides AB and AC respectively.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 116px; width: 170px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image043.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>To Prove<\/strong>: DE <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> BC<\/p>\n<p style=\"text-align: justify;\"><strong>Proof<\/strong>: Since D and E are the mid-points of AB and AC<\/p>\n<p style=\"text-align: justify;\">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\/10\/mathematics\/ch06\/Ex6.2\/image003.png\" \/>AD = DB and AE = EC<\/p>\n<p style=\"text-align: justify;\">Now, AD = DB<\/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\/10\/mathematics\/ch06\/Ex6.2\/image005.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 52px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image041.png\" \/> and AE = EC<\/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\/10\/mathematics\/ch06\/Ex6.2\/image005.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image042.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image003.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image004.png\" \/> = 1<\/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\/10\/mathematics\/ch06\/Ex6.2\/image005.png\" \/> <img decoding=\"async\" style=\"height: 41px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image004.png\" \/><\/p>\n<p style=\"text-align: justify;\">Thus, in triangle ABC, D and E are points dividing the sides AB and AC in the same ratio.<\/p>\n<p style=\"text-align: justify;\">Therefore, by the converse of Basic Proportionality theorem, we have<\/p>\n<p style=\"text-align: justify;\">DE <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> BC<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.2<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"9_ABCD_is_a_trapezium_in_which_AB_DC_and_its_diagonals_intersect_each_other_at_the_point_O_Show_that\"><\/span><strong>9. 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\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> DC and its diagonals intersect each other at the point O. Show that <img decoding=\"async\" style=\"height: 41px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image044.png\" \/> <\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. Given<\/strong>: A trapezium ABCD, in which AB <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> DC and its diagonals<\/p>\n<p style=\"text-align: justify;\">AC and BD intersect each other at O.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 96px; width: 166px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image045.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>To Prove<\/strong>: <img decoding=\"async\" style=\"height: 41px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image046.png\" \/><\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Construction_Through_O_draw_OE_AB_ie_OE_DC\"><\/span><strong>Construction<\/strong>: Through O, draw OE <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> AB, i.e. OE <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> DC.<span class=\"ez-toc-section-end\"><\/span><\/h6>\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\/10\/mathematics\/ch06\/Ex6.2\/image010.png\" \/>ADC, we have OE <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> DC<\/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\/10\/mathematics\/ch06\/Ex6.2\/image003.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image047.png\" \/> [By Basic Proportionality theorem]\u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\">Again, in <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image010.png\" \/>ABD, we have OE <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> AB[Construction]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image003.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image048.png\" \/> [By Basic Proportionality theorem]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image005.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image049.png\" \/> \u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\">From eq. (i) and (ii), we get<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 41px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image050.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\/10\/mathematics\/ch06\/Ex6.2\/image005.png\" \/> <img decoding=\"async\" style=\"height: 41px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image046.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.2<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"10_The_diagonals_of_a_quadrilateral_ABCD_intersect_each_other_at_the_point_O_such_that_Such_that_ABCD_is_a_trapezium\"><\/span><strong>10. The diagonals of a quadrilateral ABCD intersect each other at the point O such that <img decoding=\"async\" style=\"height: 41px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image044.png\" \/> Such that ABCD is a trapezium.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. Given<\/strong>: A quadrilateral ABCD, in which its diagonals AC and<\/p>\n<p style=\"text-align: justify;\">BD intersect each other at O such that <img decoding=\"async\" style=\"height: 41px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image046.png\" \/>, i.e.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 118px; width: 202px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image051.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 41px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image050.png\" \/>.<\/p>\n<p style=\"text-align: justify;\"><strong>To Prove<\/strong>: Quadrilateral ABCD is a trapezium.<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Construction_Through_O_draw_OE_AB_meeting_AD_at_E\"><\/span><strong>Construction<\/strong>: Through O, draw OE <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> AB meeting AD at E.<span class=\"ez-toc-section-end\"><\/span><\/h6>\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\/10\/mathematics\/ch06\/Ex6.2\/image010.png\" \/>ADB, we have OE <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> AB [By construction]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image003.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image052.png\" \/> [By Basic Proportionality theorem]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image005.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image053.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\/10\/mathematics\/ch06\/Ex6.2\/image005.png\" \/> <img decoding=\"async\" style=\"height: 41px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image053.png\" \/>= <img decoding=\"async\" style=\"height: 41px; width: 31px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image054.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 45px; width: 107px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image055.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\/10\/mathematics\/ch06\/Ex6.2\/image005.png\" \/> <img decoding=\"async\" style=\"height: 41px; width: 29px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image056.png\" \/>= <img decoding=\"async\" style=\"height: 41px; width: 31px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image054.png\" \/><\/p>\n<p style=\"text-align: justify;\">Thus in <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image010.png\" \/>ADC, E and O are points dividing the sides AD and AC in the same ratio. Therefore by the converse of Basic Proportionality theorem, we have<\/p>\n<p style=\"text-align: justify;\">EO <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> DC<\/p>\n<p style=\"text-align: justify;\">But EO <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> AB[By construction]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image003.png\" \/>AB <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.2\/image001.png\" \/> DC<\/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\/10\/mathematics\/ch06\/Ex6.2\/image003.png\" \/> Quadrilateral ABCD is a trapezium.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_10_Maths_Exercise_62\"><\/span>NCERT Solutions for Class 10 Maths Exercise 6.2<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>NCERT Solutions Class 10 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 10 Maths includes text book solutions from Mathematics Book. NCERT Solutions for CBSE Class 10 Maths have total 15 chapters. 10 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 10 solutions PDF and Maths ncert class 10 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_10\"><\/span>CBSE app for Class 10<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To download NCERT Solutions for Class 10 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<strong><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\">the best app for CBSE\u00a0<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions for Class 10 Maths Exercise 6.2 Class 10 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. 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