{"id":4964,"date":"2016-05-19T11:49:00","date_gmt":"2016-05-19T06:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-10-maths-exercise-6-3\/"},"modified":"2023-03-22T15:14:22","modified_gmt":"2023-03-22T09:44:22","slug":"ncert-solutions-for-class-10-maths-exercise-6-3","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-6-3\/","title":{"rendered":"NCERT Solutions for Class 10 Maths Exercise 6.3"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_76 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-6-3\/#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-for-class-10-maths-exercise-6-3\/#1_State_which_pairs_of_triangles_in_figure_are_similar_Write_the_similarity_criterion_used_by_you_for_answering_the_question_and_also_write_the_pairs_of_similar_triangles_in_the_symbolic_form\" >1. State which pairs of triangles in figure, are similar. Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form:<\/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-10-maths-exercise-6-3\/#2_In_figure_ODC_OBA_BOC_and_CDO_Find_DOC_DCO_and_OAB\" >2. In figure, ODC OBA, BOC =  and CDO =  Find DOC, DCO and OAB.<\/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-10-maths-exercise-6-3\/#3_Diagonals_AC_and_BD_of_a_trapezium_ABCD_with_AB_CD_intersect_each_other_at_the_point_O_Using_a_similarity_criterion_for_two_triangles_show_that\" >3. Diagonals AC and BD of a trapezium ABCD with AB  CD intersect each other at the point O. Using a similarity criterion for two triangles, show that<\/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-10-maths-exercise-6-3\/#4_In_figure_and_1_2_Show_that_PQS_TQR\" >4. In figure,  and 1 = 2. Show that PQS TQR.<\/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-10-maths-exercise-6-3\/#5_S_and_T_are_points_on_sides_PR_and_QR_of_a_PQR_such_that_P_RTS_Show_that_RPQ_RTS\" >5. S and T are points on sides PR and QR of a PQR such that P = RTS. Show that RPQ RTS.<\/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-10-maths-exercise-6-3\/#6_In_figure_if_ABE_ACD_show_that_ADE_ABC\" >6. In figure, if ABE ACD, show that ADE ABC.<\/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-10-maths-exercise-6-3\/#7_In_figure_altitude_AD_and_CE_of_a_ABC_intersect_each_other_at_the_point_P_Show_that\" >7. In figure, altitude AD and CE of a ABC intersect each other at the point P. Show that:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-6-3\/#8_E_is_a_point_on_the_side_AD_produced_of_a_parallelogram_ABCD_and_BE_intersects_CD_at_F_Show_that_ABE_CFB\" >8. E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that ABE CFB.<\/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-10-maths-exercise-6-3\/#9_In_figure_ABC_and_AMP_are_two_right_triangles_right_angles_at_B_and_M_respectively_Prove_that\" >9. In figure, ABC and AMP are two right triangles, right angles at B and M respectively. Prove that:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-6-3\/#10_CD_and_GH_are_respectively_the_bisectors_of_ACB_and_EGF_such_that_D_and_H_lie_on_sides_AB_and_FE_at_ABC_and_EFG_respectively_If_ABC_FEG_show_that\" >10. CD and GH are respectively the bisectors of ACB and EGF such that D and H lie on sides AB and FE at ABC and EFG respectively. If ABC FEG, 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-for-class-10-maths-exercise-6-3\/#11_In_figure_E_is_a_point_on_side_CB_produced_of_an_isosceles_triangle_ABC_with_AB_AC_If_AD_BC_and_EF_AC_prove_that_ABD_ECF\" >11. In figure, E is a point on side CB produced of an isosceles triangle ABC with AB = AC. If AD BC and EF AC, prove that ABD ECF.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-6-3\/#12_Sides_AB_and_BC_and_median_AD_of_a_triangle_ABC_are_respectively_proportional_to_sides_PQ_and_QR_and_median_PM_of_a_PQR_see_figure_Show_that_ABC_PQR\" >12. Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of a PQR (see figure). Show that ABC PQR.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-6-3\/#13_D_is_a_point_on_the_side_BC_of_a_triangle_ABC_such_that_ADC_BAC_Show_that_CA2_CBCD\" >13. D is a point on the side BC of a triangle ABC such that ADC = BAC. Show that CA2 = CB.CD.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-6-3\/#14_Sides_AB_and_AC_and_median_AD_of_a_triangle_ABC_are_respectively_proportional_to_sides_PQ_and_PR_and_median_PM_of_another_triangle_PQR_Show_that_ABC_PQR\" >14. Sides AB and AC and median AD of a triangle ABC are respectively proportional to sides PQ and PR and median PM of another triangle PQR. Show that ABC PQR.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-6-3\/#15_A_vertical_pole_of_length_6_m_casts_a_shadow_4_m_long_on_the_ground_and_at_the_same_time_a_tower_casts_a_shadow_28_m_long_Find_the_height_of_the_tower\" >15. A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-6-3\/#16_If_AD_and_PM_are_medians_of_triangles_ABC_and_PQR_respectively_where_ABC_PQR_prove_that\" >16. If AD and PM are medians of triangles ABC and PQR respectively, where ABC PQR, prove that<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-6-3\/#NCERT_Solutions_for_Class_10_Maths_Exercise_63\" >NCERT Solutions for Class 10 Maths Exercise 6.3<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-6-3\/#CBSE_app_for_Class_10\" >CBSE app for Class 10<\/a><\/li><\/ul><\/nav><\/div>\n<p>NCERT Solutions for Class 10 Maths Exercise 6.3 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<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/media-mycbseguide.s3.ap-south-1.amazonaws.com\/images\/blog\/10%20Maths%20Book.jpg\" alt=\"NCERT Solutions for Class 10 Maths Exercise 6.3\" width=\"158\" height=\"195\" \/><\/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 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"1_State_which_pairs_of_triangles_in_figure_are_similar_Write_the_similarity_criterion_used_by_you_for_answering_the_question_and_also_write_the_pairs_of_similar_triangles_in_the_symbolic_form\"><\/span><strong>1. State which pairs of triangles in figure, are similar. Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>P<\/strong><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 353px; width: 635px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image001.jpg\" \/><\/p>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 965\" style=\"height: 177px; width: 625px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image002.jpg\" \/><\/strong><\/p>\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\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>s ABC and PQR, we observe that,<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 24px; width: 352px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image004.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\/Ex6.3\/image005.png\" \/> By AAA criterion of similarity, <img decoding=\"async\" style=\"height: 21px; width: 115px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image006.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> In <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>s ABC and PQR, we observe that,<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 44px; width: 137px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image007.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\/Ex6.3\/image005.png\" \/> By SSS criterion of similarity, <img decoding=\"async\" style=\"height: 21px; width: 115px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image006.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(iii)<\/strong> In <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>s LMP and DEF, we observe that, the ratio of the sides of these triangles is not equal.<\/p>\n<p style=\"text-align: justify;\">Therefore, these two triangles are not similar.<\/p>\n<p style=\"text-align: justify;\"><strong> (iv)<\/strong> In <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>s MNL and QPR, we observe that, <img decoding=\"async\" style=\"height: 24px; width: 109px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image008.png\" \/><\/p>\n<p style=\"text-align: justify;\">But, <img decoding=\"async\" style=\"height: 44px; width: 77px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image009.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\/Ex6.3\/image005.png\" \/> These two triangles are not similar as they do not satisfy SAS criterion of similarity.<\/p>\n<p style=\"text-align: justify;\"><strong>(v)<\/strong> In <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>s ABC and FDE, we have, <img decoding=\"async\" style=\"height: 21px; width: 103px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image010.png\" \/><\/p>\n<p style=\"text-align: justify;\">But, <img decoding=\"async\" style=\"height: 41px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image011.png\" \/>[<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image012.png\" \/> AC is not 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\/10\/mathematics\/ch06\/Ex6.3\/image005.png\" \/> These two triangles are not similar as they do not satisfy SAS criterion of similarity.<\/p>\n<p style=\"text-align: justify;\"><strong> (vi)<\/strong> In <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>s DEF and PQR, we have, <img decoding=\"async\" style=\"height: 21px; width: 104px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image013.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\/Ex6.3\/image012.png\" \/> <img decoding=\"async\" style=\"height: 21px; width: 181px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image014.png\" \/>]\n<p style=\"text-align: justify;\">And <img decoding=\"async\" style=\"height: 24px; width: 104px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image015.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\/Ex6.3\/image005.png\" \/> By AAA criterion of similarity, <img decoding=\"async\" style=\"height: 21px; width: 112px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image016.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.3<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"2_In_figure_ODC_OBA_BOC_and_CDO_Find_DOC_DCO_and_OAB\"><\/span><strong>2. In figure, <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>ODC <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image017.png\" \/>OBA, <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>BOC = <img decoding=\"async\" style=\"height: 19px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image019.png\" \/> and <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>CDO = <img decoding=\"async\" style=\"height: 19px; width: 31px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image020.png\" \/> Find <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>DOC, <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>DCO and <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>OAB.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 966\" style=\"height: 125px; width: 236px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image021.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Since BD is a line and OC is a ray on it.<\/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\/Ex6.3\/image005.png\" \/> <img decoding=\"async\" style=\"height: 19px; width: 160px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image022.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\/Ex6.3\/image023.png\" \/> <img decoding=\"async\" style=\"height: 19px; width: 145px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image024.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\/Ex6.3\/image023.png\" \/> <img decoding=\"async\" style=\"height: 19px; width: 89px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image025.png\" \/><\/p>\n<p style=\"text-align: justify;\">In <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/> CDO, we have <img decoding=\"async\" style=\"height: 19px; width: 224px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image026.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\/Ex6.3\/image023.png\" \/> <img decoding=\"async\" style=\"height: 19px; width: 176px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image027.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image023.png\" \/> <img decoding=\"async\" style=\"height: 19px; width: 89px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image028.png\" \/><\/p>\n<p style=\"text-align: justify;\">It is given that <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>ODC <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image017.png\" \/>OBA<\/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\/Ex6.3\/image005.png\" \/> <img decoding=\"async\" style=\"height: 21px; width: 229px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image029.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\/Ex6.3\/image023.png\" \/> <img decoding=\"async\" style=\"height: 21px; width: 181px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image030.png\" \/><\/p>\n<p style=\"text-align: justify;\">Hence<img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>DOC = <img decoding=\"async\" style=\"height: 21px; width: 31px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image031.png\" \/> <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>DCO = <img decoding=\"async\" style=\"height: 19px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image032.png\" \/> and <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>OAB = <img decoding=\"async\" style=\"height: 19px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image032.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.3<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"3_Diagonals_AC_and_BD_of_a_trapezium_ABCD_with_AB_CD_intersect_each_other_at_the_point_O_Using_a_similarity_criterion_for_two_triangles_show_that\"><\/span><strong>3. Diagonals AC and BD of a trapezium ABCD with AB <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image033.png\" \/> CD intersect each other at the point O. Using a similarity criterion for two triangles, show that <img decoding=\"async\" style=\"height: 41px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image034.png\" \/> <\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. Given<\/strong>: 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\/Ex6.3\/image033.png\" \/>DC.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 967\" style=\"height: 96px; width: 182px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image035.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\/Ex6.3\/image036.png\" \/><\/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\/Ex6.3\/image003.png\" \/>s OAB and OCD, we have,<\/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\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>5 = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>6 [Vertically opposite angles]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>1 = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>2 [Alternate angles]\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\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>3 = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>4 [Alternate angles]\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\/Ex6.3\/image005.png\" \/> By AAA criterion of similarity,<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>OAB <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image017.png\" \/>ODC<\/p>\n<p style=\"text-align: justify;\">Hence, <img decoding=\"async\" style=\"height: 41px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image036.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.3<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"4_In_figure_and_1_2_Show_that_PQS_TQR\"><\/span><strong>4. In figure, <img decoding=\"async\" style=\"height: 44px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image037.png\" \/> and <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>1 = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>2. Show that <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>PQS <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image017.png\" \/>TQR.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 968\" style=\"height: 133px; width: 237px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image038.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>We have, <img decoding=\"async\" style=\"height: 44px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image037.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\/Ex6.3\/image023.png\" \/> <img decoding=\"async\" style=\"height: 44px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image039.png\" \/> \u2026\u2026\u2026.(1)<\/p>\n<p style=\"text-align: justify;\">Also, <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>1 = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>2 [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\/10\/mathematics\/ch06\/Ex6.3\/image005.png\" \/> PR = PQ \u2026\u2026\u2026.(2) [<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image012.png\" \/>Sides opposite to equal <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>s are equal]\n<p style=\"text-align: justify;\">From eq.(1) and (2), we get<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 44px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image039.png\" \/> <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image023.png\" \/> <img decoding=\"async\" style=\"height: 44px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image040.png\" \/><\/p>\n<p style=\"text-align: justify;\">In <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>s PQS and TQR, 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\/Ex6.3\/image040.png\" \/> and <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>PQS = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>TQR = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>Q<\/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\/Ex6.3\/image005.png\" \/> By SAS criterion of similarity,<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>PQS <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image017.png\" \/>TQR<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.3<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"5_S_and_T_are_points_on_sides_PR_and_QR_of_a_PQR_such_that_P_RTS_Show_that_RPQ_RTS\"><\/span><strong>5. S and T are points on sides PR and QR of a <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>PQR such that <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>P = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>RTS. Show that <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>RPQ <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image017.png\" \/>RTS.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\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\/Ex6.3\/image003.png\" \/>s RPQ and RTS, we have<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 7\" style=\"height: 108px; width: 125px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image041.jpg\" \/><\/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\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>RPQ = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>RTS [Given]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>PRQ = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>TRS [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\/10\/mathematics\/ch06\/Ex6.3\/image005.png\" \/> By AA-criterion of similarity,<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>RPQ <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image017.png\" \/>RTS<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.3<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"6_In_figure_if_ABE_ACD_show_that_ADE_ABC\"><\/span><strong>6. In figure, if <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>ABE <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image042.png\" \/>ACD, show that <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>ADE <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image017.png\" \/>ABC.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 970\" style=\"height: 152px; width: 143px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image043.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>It is given that <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>ABE <img decoding=\"async\" style=\"height: 17px; width: 32px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image044.png\" \/>ACD<\/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\/Ex6.3\/image005.png\" \/> AB = AC and AE = AD<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image023.png\" \/> <img decoding=\"async\" style=\"height: 41px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image045.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\/Ex6.3\/image023.png\" \/> <img decoding=\"async\" style=\"height: 41px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image046.png\" \/> \u2026\u2026\u2026.(1)<\/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\/Ex6.3\/image005.png\" \/> In <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>s ADE and ABC, we have,<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 41px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image046.png\" \/> [from eq.(1)]\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\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>BAC = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>DAE [Common]\n<p style=\"text-align: justify;\">Thus, by SAS criterion of similarity, <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>ADE <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image017.png\" \/>ABC<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.3<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"7_In_figure_altitude_AD_and_CE_of_a_ABC_intersect_each_other_at_the_point_P_Show_that\"><\/span><strong>7. In figure, altitude AD and CE of a <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>ABC intersect each other at the point P. Show that: <\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 971\" style=\"height: 131px; width: 181px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image047.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(i) <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>AEP <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image017.png\" \/>CDP<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>ABD <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image017.png\" \/>CBE<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>AEP <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image017.png\" \/>ADB<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iv) <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>PDC <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image017.png\" \/>BEC<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>(i) In <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>s AEP and CDP, we have,<\/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\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>AEP = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>CDP = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image048.png\" \/> [<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image012.png\" \/> CE<img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image049.png\" \/>AB, AD<img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image049.png\" \/>BC]\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\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>APE = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>CPD[ Vertically opposite]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image005.png\" \/> By AA-criterion of similarity, <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>AEP <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image017.png\" \/>CDP<\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> In <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>s ABD and CBE, we have,<\/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\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>ADB = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>CEB = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image048.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\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>ABD = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>CBE[ 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\/10\/mathematics\/ch06\/Ex6.3\/image005.png\" \/> By AA-criterion of similarity, <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>ABD <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image017.png\" \/>CBE<\/p>\n<p style=\"text-align: justify;\"><strong>(iii)<\/strong> In <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>s AEP and ADB, we have,<\/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\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>AEP = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>ADB = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image048.png\" \/> [<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image012.png\" \/> AD<img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image049.png\" \/>BC, CE<img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image049.png\" \/>AB]\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\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>PAE = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>DAB[ 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\/10\/mathematics\/ch06\/Ex6.3\/image005.png\" \/> By AA-criterion of similarity, <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>AEP <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image017.png\" \/>ADB<\/p>\n<p style=\"text-align: justify;\"><strong>(iv)<\/strong> In <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>s PDC and BEC, we have,<\/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\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>PDC = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>BEC = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image048.png\" \/> [<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image012.png\" \/> CE<img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image049.png\" \/>AB, AD<img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image049.png\" \/>BC]\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\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>PCD = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>BEC[ 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\/10\/mathematics\/ch06\/Ex6.3\/image005.png\" \/> By AA-criterion of similarity, <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>PDC <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image017.png\" \/>BEC<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.3<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"8_E_is_a_point_on_the_side_AD_produced_of_a_parallelogram_ABCD_and_BE_intersects_CD_at_F_Show_that_ABE_CFB\"><\/span><strong>8. E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>ABE <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image017.png\" \/>CFB.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\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\/Ex6.3\/image003.png\" \/>s ABE and CFB, we have,<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 16\" style=\"height: 92px; width: 164px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image050.jpg\" \/><\/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\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>AEB = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>CBF[Alt. <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>s]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>A = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>C [opp. <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>s of a <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image033.png\" \/>gm]\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\/Ex6.3\/image005.png\" \/> By AA-criterion of similarity, we have<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>ABE <img decoding=\"async\" style=\"height: 11px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image051.png\" \/> <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>CFB<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.3<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"9_In_figure_ABC_and_AMP_are_two_right_triangles_right_angles_at_B_and_M_respectively_Prove_that\"><\/span><strong>9. In figure, ABC and AMP are two right triangles, right angles at B and M respectively. Prove that:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 972\" style=\"height: 109px; width: 135px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image052.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(i) <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>ABC <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image017.png\" \/>AMP<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <img decoding=\"async\" style=\"height: 41px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image053.png\" \/> <\/strong><\/p>\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\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>s ABC and AMP, we have,<\/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\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>ABC = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>AMP = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image048.png\" \/> [Given]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>BAC = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>MAP [Common angles]\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\/Ex6.3\/image005.png\" \/> By AA-criterion of similarity, we have<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>ABC <img decoding=\"async\" style=\"height: 11px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image051.png\" \/> <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>AMP<\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> We have <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>ABC <img decoding=\"async\" style=\"height: 11px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image051.png\" \/> <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>AMP [As prove above]\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\/Ex6.3\/image023.png\" \/> <img decoding=\"async\" style=\"height: 41px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image053.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.3<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"10_CD_and_GH_are_respectively_the_bisectors_of_ACB_and_EGF_such_that_D_and_H_lie_on_sides_AB_and_FE_at_ABC_and_EFG_respectively_If_ABC_FEG_show_that\"><\/span><strong>10. CD and GH are respectively the bisectors of <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>ACB and <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>EGF such that D and H lie on sides AB and FE at <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>ABC and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>EFG respectively. If <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>ABC <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image017.png\" \/>FEG, show that:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(i) <img decoding=\"async\" style=\"height: 41px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image054.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>DCB <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image017.png\" \/>HE<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>DCA <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image017.png\" \/>HGF<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>We have, <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>ABC <img decoding=\"async\" style=\"height: 11px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image051.png\" \/> <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>FEG<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 22\" style=\"height: 128px; width: 223px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image055.jpg\" \/><\/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\/Ex6.3\/image023.png\" \/> <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>A = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>F\u2026\u2026\u2026(1)<\/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\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>C = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>G<\/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\/Ex6.3\/image023.png\" \/> <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image056.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>C = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image056.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>G<\/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\/Ex6.3\/image023.png\" \/> <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>1 = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>3 and <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>2 = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>4 \u2026\u2026\u2026.(2)<\/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\/Ex6.3\/image012.png\" \/>CD and GH are bisectors of <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>C and <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>G<\/p>\n<p style=\"text-align: justify;\">respectively]\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\/Ex6.3\/image005.png\" \/> In <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>s DCA and HGF, we have<\/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\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>A = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>F[From eq.(1)]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>2 = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>4[From eq.(2)]\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\/Ex6.3\/image005.png\" \/> By AA-criterion of similarity, we have<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>DCA <img decoding=\"async\" style=\"height: 11px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image051.png\" \/> <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>HGF<\/p>\n<p style=\"text-align: justify;\">Which proves the (iii) part<\/p>\n<p style=\"text-align: justify;\">We have,<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>DCA <img decoding=\"async\" style=\"height: 11px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image051.png\" \/> <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>HGF<\/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\/Ex6.3\/image023.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image057.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\/Ex6.3\/image023.png\" \/> <img decoding=\"async\" style=\"height: 41px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image054.png\" \/><\/p>\n<p style=\"text-align: justify;\">Which proves the (i) part<\/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\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>s DCA and HGF, we have<\/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\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>1 = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>3[From eq.(2)]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>B = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>E[<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image012.png\" \/> <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>DCB <img decoding=\"async\" style=\"height: 11px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image051.png\" \/> <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>HE]\n<p style=\"text-align: justify;\">Which proves the (ii) part<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.3<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"11_In_figure_E_is_a_point_on_side_CB_produced_of_an_isosceles_triangle_ABC_with_AB_AC_If_AD_BC_and_EF_AC_prove_that_ABD_ECF\"><\/span><strong>11. In figure, E is a point on side CB produced of an isosceles triangle ABC with AB = AC. If AD<img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image049.png\" \/> BC and EF<img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image049.png\" \/> AC, prove that <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>ABD <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image017.png\" \/>ECF.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 973\" style=\"height: 154px; width: 146px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image058.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Here <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>ABC is isosceles with AB = 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\/Ex6.3\/image005.png\" \/> <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>B = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>C<\/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\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>s ABD and ECF, we have<\/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\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>ABD = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>ECF[<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image012.png\" \/> <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>B = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>C]\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>ABD = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>ECF = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image048.png\" \/> [<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image012.png\" \/> AD<img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image049.png\" \/>BC and EF<img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image049.png\" \/>AC]\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\/Ex6.3\/image005.png\" \/> By AA-criterion of similarity, we have<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>ABD <img decoding=\"async\" style=\"height: 11px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image051.png\" \/> <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>ECF<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.3<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"12_Sides_AB_and_BC_and_median_AD_of_a_triangle_ABC_are_respectively_proportional_to_sides_PQ_and_QR_and_median_PM_of_a_PQR_see_figure_Show_that_ABC_PQR\"><\/span><strong>12. Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of a <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>PQR (see figure). Show that <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>ABC <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image017.png\" \/>PQR.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 974\" style=\"height: 112px; width: 299px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image059.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. Given<\/strong>: AD is the median of <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/> ABC and PM is the median of <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/> PQR such that<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 44px; width: 113px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image060.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>To prove<\/strong>: <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/> ABC <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image017.png\" \/> PQR<\/p>\n<p style=\"text-align: justify;\"><strong>Proof<\/strong>: BD = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image056.png\" \/>BC [Given]\n<p style=\"text-align: justify;\">And QM = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image056.png\" \/>QR [Given]\n<p style=\"text-align: justify;\">Also <img decoding=\"async\" style=\"height: 44px; width: 113px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image060.png\" \/>[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\/Ex6.3\/image023.png\" \/><img decoding=\"async\" style=\"height: 44px; width: 124px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image061.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\/Ex6.3\/image023.png\" \/><img decoding=\"async\" style=\"height: 44px; width: 116px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image062.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\/Ex6.3\/image005.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>ABD <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image017.png\" \/>PQM[By SSS-criterion of similarity]\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\/Ex6.3\/image023.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>B = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>Q[Similar triangles have corresponding angles equal]\n<p style=\"text-align: justify;\">And <img decoding=\"async\" style=\"height: 44px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image063.png\" \/>[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\/10\/mathematics\/ch06\/Ex6.3\/image005.png\" \/>By SAS-criterion of similarity, we have<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>ABC <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image017.png\" \/>PQR<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.3<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"13_D_is_a_point_on_the_side_BC_of_a_triangle_ABC_such_that_ADC_BAC_Show_that_CA2_CBCD\"><\/span><strong>13. D is a point on the side BC of a triangle ABC such that <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>ADC = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>BAC. Show that CA<sup>2<\/sup> = CB.CD.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>ANS. <\/strong>In triangles ABC and DAC,<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 31\" style=\"height: 143px; width: 137px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image064.jpg\" \/><\/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\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>ADC = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>BAC [Given]\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\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>C = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>C[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\/10\/mathematics\/ch06\/Ex6.3\/image005.png\" \/>By AA-similarity criterion,<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>ABC <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image017.png\" \/>DAC<\/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\/Ex6.3\/image023.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 112px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image065.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\/Ex6.3\/image023.png\" \/> <img decoding=\"async\" style=\"height: 41px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image066.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\/Ex6.3\/image023.png\" \/> <img decoding=\"async\" style=\"height: 22px; width: 31px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image067.png\" \/>= CB.CD<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.3<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"14_Sides_AB_and_AC_and_median_AD_of_a_triangle_ABC_are_respectively_proportional_to_sides_PQ_and_PR_and_median_PM_of_another_triangle_PQR_Show_that_ABC_PQR\"><\/span><strong>14. Sides AB and AC and median AD of a triangle ABC are respectively proportional to sides PQ and PR and median PM of another triangle PQR. Show that <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>ABC <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image017.png\" \/>PQR.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>ANS. Given<\/strong>: AD is the median of <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/> ABC and PM is the median of <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/> PQR such that<\/p>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 28\" style=\"height: 110px; width: 299px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image068.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 44px; width: 113px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image060.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>To prove<\/strong>: <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/> ABC <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image017.png\" \/> PQR<\/p>\n<p style=\"text-align: justify;\"><strong>Proof<\/strong>: BD = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image056.png\" \/>BC [Given]\n<p style=\"text-align: justify;\">And QM = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image056.png\" \/>QR and <img decoding=\"async\" style=\"height: 44px; width: 113px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image060.png\" \/>[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\/Ex6.3\/image023.png\" \/><img decoding=\"async\" style=\"height: 44px; width: 124px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image061.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\/Ex6.3\/image023.png\" \/><img decoding=\"async\" style=\"height: 44px; width: 116px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image062.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\/Ex6.3\/image005.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>ABD <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image017.png\" \/>PQM[By SSS-criterion of similarity]\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\/Ex6.3\/image023.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>B = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>Q[Similar triangles have corresponding angles equal]\n<p style=\"text-align: justify;\">And <img decoding=\"async\" style=\"height: 44px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image063.png\" \/>[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\/10\/mathematics\/ch06\/Ex6.3\/image005.png\" \/>By SAS-criterion of similarity, we have<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>ABC <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image017.png\" \/>PQR<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.3<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"15_A_vertical_pole_of_length_6_m_casts_a_shadow_4_m_long_on_the_ground_and_at_the_same_time_a_tower_casts_a_shadow_28_m_long_Find_the_height_of_the_tower\"><\/span><strong>15. A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let AB the vertical pole and AC be its shadow. Also, let DE be the vertical tower and DF be its shadow. Joined BC and EF.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 34\" style=\"height: 121px; width: 122px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image069.jpg\" \/><\/p>\n<p style=\"text-align: justify;\">Let DE = <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image070.png\" \/> meters<\/p>\n<p style=\"text-align: justify;\">Here, AB = 6 m, AC = 4 m and DF = 28 m<\/p>\n<p style=\"text-align: justify;\">In the triangles ABC and DEF,<\/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\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>A = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>D = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image048.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\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>C = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>F[Each is the angular elevation of the sun]\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 37\" style=\"height: 142px; width: 125px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image071.jpg\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image005.png\" \/>By AA-similarity criterion,<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>ABC <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image017.png\" \/>DEF<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image023.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image072.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\/Ex6.3\/image023.png\" \/> <img decoding=\"async\" style=\"height: 41px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image073.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\/Ex6.3\/image023.png\" \/> <img decoding=\"async\" style=\"height: 41px; width: 43px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image074.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\/Ex6.3\/image023.png\" \/> <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image070.png\" \/> = 42 m<\/p>\n<p style=\"text-align: justify;\">Hence, the height of the tower is 42 meters.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.3<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"16_If_AD_and_PM_are_medians_of_triangles_ABC_and_PQR_respectively_where_ABC_PQR_prove_that\"><\/span><strong>16. If AD and PM are medians of triangles ABC and PQR respectively, where <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>ABC <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image017.png\" \/>PQR, prove that <img decoding=\"async\" style=\"height: 44px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image075.png\" \/> <\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. Given<\/strong>: AD and PM are the medians of triangles<\/p>\n<p style=\"text-align: justify;\">ABC and PQR respectively, where<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 128px; width: 272px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image076.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>ABC <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image017.png\" \/>PQR<\/p>\n<p style=\"text-align: justify;\"><strong>To prove<\/strong>: <img decoding=\"async\" style=\"height: 44px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image077.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Proof:<\/strong> In triangles ABD and PQM,<\/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\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>B = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image018.png\" \/>Q [Given]\n<p style=\"text-align: justify;\">And <img decoding=\"async\" style=\"height: 80px; width: 83px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image078.png\" \/>[<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image012.png\" \/> AD and PM are the medians of BC and QR respectively]\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\/Ex6.3\/image023.png\" \/><img decoding=\"async\" style=\"height: 44px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image079.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\/Ex6.3\/image005.png\" \/>By SAS-criterion of similarity,<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image003.png\" \/>ABD <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image017.png\" \/>PQM<\/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\/Ex6.3\/image023.png\" \/> <img decoding=\"async\" style=\"height: 44px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image079.png\" \/> = <img decoding=\"async\" style=\"height: 41px; width: 31px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image080.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\/Ex6.3\/image023.png\" \/> <img decoding=\"async\" style=\"height: 44px; width: 29px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image081.png\" \/> = <img decoding=\"async\" style=\"height: 41px; width: 31px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.3\/image080.png\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_10_Maths_Exercise_63\"><\/span>NCERT Solutions for Class 10 Maths Exercise 6.3<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<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\u00a0<\/strong><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions for Class 10 Maths Exercise 6.3 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 &#8230; <a title=\"NCERT Solutions for Class 10 Maths Exercise 6.3\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-6-3\/\" aria-label=\"More on NCERT Solutions for Class 10 Maths Exercise 6.3\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":29985,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1347,281],"tags":[1042,216],"class_list":["post-4964","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics","category-ncert-solutions","tag-cbse-class-10-mathematics","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 10 Maths Exercise 6.3 | myCBSEguide<\/title>\n<meta name=\"description\" content=\"NCERT Solutions for Class 10 Maths Exercise 6.3 in PDF format for free download. 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