{"id":4965,"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-6-4\/"},"modified":"2023-03-22T15:14:37","modified_gmt":"2023-03-22T09:44:37","slug":"ncert-solutions-for-class-10-maths-exercise-6-4","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-6-4\/","title":{"rendered":"NCERT Solutions for Class 10 Maths Exercise 6.4"},"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-6-4\/#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-6-4\/#1_Let_ABC_DEF_and_their_areas_be_respectively_64_cm2_and_121_cm2_If_EF_154_cm_find_BC\" >1. Let ABC DEF and their areas be, respectively, 64 cm2 and 121 cm2. If EF = 15.4 cm, find BC.<\/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-6-4\/#2_Diagonals_of_a_trapezium_ABCD_with_AB_DC_intersect_each_other_at_the_point_O_If_AB_2CD_find_the_ratio_of_the_areas_of_triangles_AOB_and_COD\" >2. Diagonals of a trapezium ABCD with AB  DC intersect each other at the point O. If AB = 2CD, find the ratio of the areas of triangles AOB and COD.<\/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-6-4\/#3_In_figure_ABC_and_DBC_are_two_triangles_on_the_same_base_BC_If_AD_intersects_BC_at_O_show_that\" >3. In figure, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, 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-6-4\/#4_If_the_areas_of_two_similar_triangles_are_equal_prove_that_they_are_congruent\" >4. If the areas of two similar triangles are equal, prove that they are congruent.<\/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-6-4\/#5_D_E_and_F_are_respectively_the_mid-points_of_sides_AB_BC_and_CA_of_ABC_Find_the_ratio_of_the_areas_of_DEF_and_ABC\" >5. D, E and F are respectively the mid-points of sides AB, BC and CA of ABC. Find the ratio of the areas of DEF and ABC.<\/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-6-4\/#6_Prove_that_the_ratio_of_the_areas_of_two_similar_triangles_is_equal_to_the_square_of_the_ratio_of_their_corresponding_medians\" >6. Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.<\/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-6-4\/#7_Prove_that_the_area_of_an_equilateral_triangle_described_on_one_side_of_a_square_is_equal_to_half_the_area_of_the_equilateral_triangle_described_on_one_of_the_diagonals\" >7. Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of the diagonals.<\/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-6-4\/#8_ABC_and_BDE_are_two_equilateral_triangles_such_that_D_is_the_mid-point_of_BC_Ratio_of_the_areas_of_triangles_ABC_and_BDE_is\" >8. ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the areas of triangles ABC and BDE is:<\/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-6-4\/#9_Sides_of_two_similar_triangles_are_in_the_ratio_4_9_Areas_of_these_triangles_are_in_the_ratio\" >9. Sides of two similar triangles are in the ratio 4 : 9. Areas of these triangles are in the ratio:<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-6-4\/#NCERT_Solutions_for_Class_10_Maths_Exercise_64\" >NCERT Solutions for Class 10 Maths Exercise 6.4<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-6-4\/#CBSE_app_for_Class_10\" >CBSE app for Class 10<\/a><\/li><\/ul><\/nav><\/div>\n<p>NCERT Solutions for Class 10 Maths Exercise 6.4 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 6.4\" width=\"178\" height=\"219\" \/><\/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_Let_ABC_DEF_and_their_areas_be_respectively_64_cm2_and_121_cm2_If_EF_154_cm_find_BC\"><\/span><strong>1. Let <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>ABC <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image002.png\" \/>DEF and their areas be, respectively, 64 cm<sup>2<\/sup> and 121 cm<sup>2<\/sup>. If EF = 15.4 cm, find BC.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>We have, <img decoding=\"async\" style=\"height: 49px; width: 145px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image003.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\/Ex6.4\/image004.png\" \/> <img decoding=\"async\" style=\"height: 52px; width: 92px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image005.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\/Ex6.4\/image004.png\" \/> <img decoding=\"async\" style=\"height: 41px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image006.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image004.png\" \/> BC = <img decoding=\"async\" style=\"height: 45px; width: 75px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image007.png\" \/>cm = 11.2 cm<\/p>\n<hr \/>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"2_Diagonals_of_a_trapezium_ABCD_with_AB_DC_intersect_each_other_at_the_point_O_If_AB_2CD_find_the_ratio_of_the_areas_of_triangles_AOB_and_COD\"><\/span><strong>2. Diagonals 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\/Ex6.4\/image008.png\" \/> DC intersect each other at the point O. If AB = 2CD, find the ratio of the areas of triangles AOB and COD.<\/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\/Ex6.4\/image001.png\" \/>s AOB and COD, we have,<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 1\" style=\"height: 102px; width: 138px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image009.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\/Ex6.4\/image010.png\" \/>AOB = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image010.png\" \/>COD[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\/Ex6.4\/image010.png\" \/>OAB = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image010.png\" \/>OCD[Alternate angles]\n<p style=\"text-align: justify;\">By AA-criterion of similarity,<\/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\/Ex6.4\/image011.png\" \/> <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>AOB<img decoding=\"async\" style=\"height: 11px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image012.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>COD<\/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\/Ex6.4\/image011.png\" \/> <img decoding=\"async\" style=\"height: 49px; width: 148px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image013.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\/Ex6.4\/image004.png\" \/> <img decoding=\"async\" style=\"height: 49px; width: 193px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image014.png\" \/><\/p>\n<p style=\"text-align: justify;\">Hence, Area (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>AOB) : Area (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>COD) = 4 : 1<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.4<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"3_In_figure_ABC_and_DBC_are_two_triangles_on_the_same_base_BC_If_AD_intersects_BC_at_O_show_that\"><\/span><strong>3. In figure, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that <img decoding=\"async\" style=\"height: 49px; width: 123px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image015.png\" \/> <\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 47\" style=\"height: 131px; width: 196px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image016.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. Given<\/strong>: Two <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>s ABC and DBC which stand on the same base but on the opposite sides of BC.<\/p>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 7\" style=\"height: 93px; width: 164px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image017.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>To Prove<\/strong>: <img decoding=\"async\" style=\"height: 49px; width: 141px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image018.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Construction<\/strong>: Draw AE<img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image019.png\" \/>BC and DF<img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image019.png\" \/>BC.<\/p>\n<p style=\"text-align: justify;\"><strong>Proof<\/strong>: In <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>s AOE and DOF, we have, <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image010.png\" \/>AEO = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image010.png\" \/>DFO = <img decoding=\"async\" style=\"height: 21px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image020.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\/Ex6.4\/image010.png\" \/>AOE = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image010.png\" \/>DOF[Vertically opposite)<\/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\/Ex6.4\/image011.png\" \/> <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>AOE<img decoding=\"async\" style=\"height: 11px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image012.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>DOF[By AA-criterion]\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\/Ex6.4\/image011.png\" \/> <img decoding=\"async\" style=\"height: 41px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image021.png\" \/> \u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\">Now, <img decoding=\"async\" style=\"height: 80px; width: 196px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/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\/Ex6.4\/image004.png\" \/> <img decoding=\"async\" style=\"height: 49px; width: 140px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image023.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\/Ex6.4\/image004.png\" \/> <img decoding=\"async\" style=\"height: 49px; width: 141px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image024.png\" \/>[using eq. (i)]\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.4<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"4_If_the_areas_of_two_similar_triangles_are_equal_prove_that_they_are_congruent\"><\/span><strong>4. If the areas of two similar triangles are equal, prove that they are congruent.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. Given<\/strong>: Two <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>s ABC and DEF such that <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>ABC<img decoding=\"async\" style=\"height: 11px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image012.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>DEF<\/p>\n<p style=\"text-align: justify;\">And Area(<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>ABC) = Area (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>DEF)<\/p>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 51\" style=\"height: 96px; width: 238px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image025.jpg\" \/><\/strong><\/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\/Ex6.4\/image001.png\" \/>ABC<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image026.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>DEF<\/p>\n<p style=\"text-align: justify;\"><strong>Proof<\/strong>: <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>ABC<img decoding=\"async\" style=\"height: 11px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image012.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>DEF<\/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\/Ex6.4\/image011.png\" \/> <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image010.png\" \/>A = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image010.png\" \/>D, <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image010.png\" \/>B = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image010.png\" \/>E, <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image010.png\" \/>C = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image010.png\" \/>F<\/p>\n<p style=\"text-align: justify;\">And <img decoding=\"async\" style=\"height: 41px; width: 109px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image027.png\" \/><\/p>\n<p style=\"text-align: justify;\">To establish <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>ABC<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image026.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>DEF, it is sufficient to prove that, AB = DE, BC = EF and AC = DF<\/p>\n<p style=\"text-align: justify;\">Now, Area(<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>ABC) = Area (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>DEF)<\/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\/Ex6.4\/image011.png\" \/> <img decoding=\"async\" style=\"height: 49px; width: 120px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image028.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\/Ex6.4\/image004.png\" \/> <img decoding=\"async\" style=\"height: 44px; width: 129px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image029.png\" \/>= 1<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image004.png\" \/> <img decoding=\"async\" style=\"height: 41px; width: 109px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image027.png\" \/>= 1<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image004.png\" \/> AB = DE, BC = EF, AC = DF<\/p>\n<p style=\"text-align: justify;\">Hence,<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>ABC<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image026.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>DEF<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.4<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"5_D_E_and_F_are_respectively_the_mid-points_of_sides_AB_BC_and_CA_of_ABC_Find_the_ratio_of_the_areas_of_DEF_and_ABC\"><\/span><strong>5. D, E and F are respectively the mid-points of sides AB, BC and CA of <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>ABC. Find the ratio of the areas of <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>DEF and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>ABC.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Since, D and E are the mid-points of the sides BC and CA of <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>ABC respectively.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image011.png\" \/> DE<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image008.png\" \/>BA <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image004.png\" \/> DE<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image008.png\" \/>FA \u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\">Since, D and F are the mid-points of the sides BC and AB of <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>ABC respectively.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image011.png\" \/> DF<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image008.png\" \/>CA <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image004.png\" \/> DE<img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image008.png\" \/>AE \u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 52\" style=\"height: 114px; width: 133px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image030.jpg\" \/><\/p>\n<p style=\"text-align: justify;\">From (i) and (ii), we can say that AFDE is a parallelogram.<\/p>\n<p style=\"text-align: justify;\">Similarly, BDEF is a parallelogram.<\/p>\n<p style=\"text-align: justify;\">Now, in <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>s DEF and ABC, 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\/Ex6.4\/image010.png\" \/>FDE = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image010.png\" \/>A[opposite angles of <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image008.png\" \/>gm AFDE]\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\/Ex6.4\/image010.png\" \/>DEF = <img decoding=\"async\" style=\"height: 16px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image010.png\" \/>B[opposite angles of <img decoding=\"async\" style=\"height: 21px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image008.png\" \/>gm BDEF]\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\/Ex6.4\/image011.png\" \/> By AA-criterion of similarity, we have <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>DEF <img decoding=\"async\" style=\"height: 11px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image012.png\" \/> <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>ABC<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image004.png\" \/> <img decoding=\"async\" style=\"height: 72px; width: 233px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image031.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\/Ex6.4\/image032.png\" \/> DE = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image033.png\" \/>AB]\n<p style=\"text-align: justify;\">Hence, Area (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>DEF): Area (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>ABC) = 1 : 4<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.4<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"6_Prove_that_the_ratio_of_the_areas_of_two_similar_triangles_is_equal_to_the_square_of_the_ratio_of_their_corresponding_medians\"><\/span><strong>6. Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. Given<\/strong>: <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>ABC<img decoding=\"async\" style=\"height: 11px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image012.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>PQR, AD and PM are the medians of <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>s ABC and PQR respectively.<\/p>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 53\" style=\"height: 101px; width: 251px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image034.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>To Prove<\/strong>: <strong><img decoding=\"async\" style=\"height: 47px; width: 144px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image035.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Proof<\/strong>: Since <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>ABC<img decoding=\"async\" style=\"height: 11px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image012.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>PQR<\/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\/Ex6.4\/image011.png\" \/> <strong><img decoding=\"async\" style=\"height: 47px; width: 143px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image036.png\" \/><\/strong>\u2026\u2026\u2026.(1)<\/p>\n<p style=\"text-align: justify;\">But, <img decoding=\"async\" style=\"height: 44px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image037.png\" \/> \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\/Ex6.4\/image011.png\" \/> From eq. (1) and (2), we have,<\/p>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" style=\"height: 47px; width: 144px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image035.png\" \/><\/strong><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.4<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"7_Prove_that_the_area_of_an_equilateral_triangle_described_on_one_side_of_a_square_is_equal_to_half_the_area_of_the_equilateral_triangle_described_on_one_of_the_diagonals\"><\/span><strong>7. Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of the diagonals.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Tick the correct answer and justify:<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. Given<\/strong>: A square ABCD,<\/p>\n<p style=\"text-align: justify;\">Equilateral <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>s BCE and ACF have been drawn on side BC and the diagonal AC respectively.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 54\" style=\"height: 135px; width: 189px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image038.jpg\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>To Prove<\/strong>: Area (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>BCE) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image033.png\" \/>Area (<img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>ACF)<\/p>\n<p style=\"text-align: justify;\"><strong>Proof<\/strong>: <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>BCE<img decoding=\"async\" style=\"height: 11px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image012.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>ACF<\/p>\n<p style=\"text-align: justify;\">[Being equilateral so similar by AAA criterion of<\/p>\n<p style=\"text-align: justify;\">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\/Ex6.4\/image004.png\" \/> <strong><img decoding=\"async\" style=\"height: 47px; width: 141px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image039.png\" \/><\/strong><\/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\/Ex6.4\/image004.png\" \/> <strong><img decoding=\"async\" style=\"height: 59px; width: 171px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image040.png\" \/><\/strong><\/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\/Ex6.4\/image032.png\" \/> Diagonal = <img decoding=\"async\" style=\"height: 23px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image041.png\" \/>side <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image004.png\" \/> AC = <img decoding=\"async\" style=\"height: 23px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image041.png\" \/>BC]\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\/Ex6.4\/image004.png\" \/> <strong><img decoding=\"async\" style=\"height: 44px; width: 120px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image042.png\" \/><\/strong><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.4<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"8_ABC_and_BDE_are_two_equilateral_triangles_such_that_D_is_the_mid-point_of_BC_Ratio_of_the_areas_of_triangles_ABC_and_BDE_is\"><\/span><strong>8. ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the areas of triangles ABC and BDE is:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(A) 2: 1 <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(B) 1: 2<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(C) 4: 1<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(D) 1: 4<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (C)<\/strong> Since <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>ABC and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>BDE are equilateral, they are equiangular and hence,<\/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\/Ex6.4\/image001.png\" \/>ABC<img decoding=\"async\" style=\"height: 11px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image012.png\" \/><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image001.png\" \/>BDE<\/p>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 56\" style=\"height: 132px; width: 127px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image043.jpg\" \/><\/strong><\/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\/Ex6.4\/image004.png\" \/> <strong><img decoding=\"async\" style=\"height: 47px; width: 143px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image044.png\" \/><\/strong><\/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\/Ex6.4\/image004.png\" \/> <strong><img decoding=\"async\" style=\"height: 47px; width: 161px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image045.png\" \/> <\/strong><\/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\/Ex6.4\/image032.png\" \/>D is the mid-point of BC]\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\/Ex6.4\/image004.png\" \/> <strong><img decoding=\"async\" style=\"height: 44px; width: 121px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image046.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image011.png\" \/> <\/strong>(C) is the correct answer.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 6.4<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"9_Sides_of_two_similar_triangles_are_in_the_ratio_4_9_Areas_of_these_triangles_are_in_the_ratio\"><\/span><strong>9. Sides of two similar triangles are in the ratio 4 : 9. Areas of these triangles are in the ratio:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(A) 2: 3 <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(B) 4: 9<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(C) 81: 16<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(D) 16: 81<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (D)<\/strong> Since the ratio of the areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides. Therefore,<\/p>\n<p style=\"text-align: justify;\">Ratio of areas = <img decoding=\"async\" style=\"height: 56px; width: 67px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image047.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch06\/Ex6.4\/image011.png\" \/> <\/strong>(D) is the correct answer.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_10_Maths_Exercise_64\"><\/span>NCERT Solutions for Class 10 Maths Exercise 6.4<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>NCERT Solutions Class 10 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 10 Maths includes text book solutions from Mathematics Book. NCERT Solutions for CBSE Class 10 Maths have total 15 chapters. 10 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 10 solutions PDF and Maths ncert class 10 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_app_for_Class_10\"><\/span>CBSE app for Class 10<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To download NCERT Solutions for Class 10 Maths, Computer Science, Home Science,Hindi ,English, Social Science do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through\u00a0<strong><a href=\"https:\/\/play.google.com\/store\/apps\/details?id=in.techchefs.MyCBSEGuide&amp;referrer=utm_source%3Dmycbse_bottom%26utm_medium%3Dtext%26utm_campaign%3Dmycbseads\">the best app for CBSE\u00a0<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions for Class 10 Maths Exercise 6.4 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 6.4\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-6-4\/\" aria-label=\"More on NCERT Solutions for Class 10 Maths Exercise 6.4\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":29986,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1347,281],"tags":[1042,283,438,321,1485,216],"class_list":["post-4965","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics","category-ncert-solutions","tag-cbse-class-10-mathematics","tag-cbse-study-material","tag-class-10","tag-mathematics","tag-maths","tag-ncert-solutions"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>NCERT Solutions for Class 10 Maths Exercise 6.4 | myCBSEguide<\/title>\n<meta name=\"description\" content=\"NCERT Solutions for Class 10 Maths Exercise 6.4 in PDF format for free download. 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