{"id":4307,"date":"2016-05-13T11:49:00","date_gmt":"2016-05-13T06:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-7-maths-triangles-and-its-properties-ex-6-4\/"},"modified":"2018-07-07T11:04:39","modified_gmt":"2018-07-07T05:34:39","slug":"ncert-solutions-for-class-7-maths-exercise-6-4","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-7-maths-exercise-6-4\/","title":{"rendered":"NCERT Solutions for Class 7 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-7-maths-exercise-6-4\/#NCERT_Solutions_for_Class_7_Maths_Triangles_and_its_Properties\" >NCERT Solutions for Class 7 Maths\u00a0Triangles and its Properties<\/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-7-maths-exercise-6-4\/#Class_%E2%80%93VII_Mathematics_Ex_64\" >Class \u2013VII Mathematics (Ex. 6.4)<\/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-7-maths-exercise-6-4\/#Question_1Is_it_possible_to_have_a_triangle_with_the_following_sides\" >Question 1.Is it possible to have a triangle with the following sides?<\/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-7-maths-exercise-6-4\/#Question_2Take_any_point_O_in_the_interior_of_a_triangle_PQR_Is\" >Question 2.Take any point O in the interior of a triangle PQR. Is:<\/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-7-maths-exercise-6-4\/#Question_3AM_is_a_median_of_a_triangle_ABC_Is_AB_BC_CA_%3E_2AM\" >Question 3.AM is a median of a triangle ABC. Is AB + BC + CA &gt; 2AM ?<\/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-7-maths-exercise-6-4\/#Question_4ABCD_is_a_quadrilateral_Is_AB_BC_CD_DA_%3E_AC_BD\" >Question 4.ABCD is a quadrilateral. Is AB + BC + CD + DA &gt; AC + BD ?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-7-maths-exercise-6-4\/#Question_6The_lengths_of_two_sides_of_a_triangle_are_12_cm_and_15_cm_Between_what_two_measures_should_the_length_of_the_third_side_fall\" >Question 6.The lengths of two sides of a triangle are 12 cm and 15 cm. Between what two measures should the length of the third side fall?<\/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-8\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-7-maths-exercise-6-4\/#NCERT_Solutions_for_Class_7_Maths_Exercise_64\" >NCERT Solutions for Class 7 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-9\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-7-maths-exercise-6-4\/#CBSE_app_for_Students\" >CBSE app for Students<\/a><\/li><\/ul><\/nav><\/div>\n<p>NCERT Solutions for Class 7 Maths Exercise 6.4 book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 7 Maths chapter wise NCERT solution for Maths Book 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\u00a0Triangles and its Properties\u00a0<\/strong><strong><a class=\"button\" href=\"https:\/\/mycbseguide.com\/downloads\/cbse-class-07-mathematics-the-triangle-and-its-properties\/1515\/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\/07_Maths_Book.jpg\" alt=\"NCERT Solutions for Class 7 Maths Exercise 6.4\" width=\"162\" height=\"205\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_7_Maths_Triangles_and_its_Properties\"><\/span>NCERT Solutions for Class 7 Maths\u00a0Triangles and its Properties<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h6 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"Class_%E2%80%93VII_Mathematics_Ex_64\"><\/span><strong>Class \u2013VII Mathematics (Ex. 6.4)<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<h6><span class=\"ez-toc-section\" id=\"Question_1Is_it_possible_to_have_a_triangle_with_the_following_sides\"><\/span><strong>Question 1.<\/strong>Is it possible to have a triangle with the following sides?<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<ol>\n<li>2 cm, 3 cm, 5 cm<\/li>\n<li>3 cm, 6 cm, 7 cm<\/li>\n<li>6 cm, 3 cm, 2 cm<\/li>\n<\/ol>\n<p><strong>Answer:<\/strong><\/p>\n<p>Since, a triangle is possible whose sum of the lengths of any two sides would be greater than the length of third side.<\/p>\n<p>(i) 2 cm, 3 cm, 5 cm<\/p>\n<p>2 + 3 &gt; 5 No<\/p>\n<p>2 + 5 &gt; 3 Yes<\/p>\n<p>3 + 5 &gt; 2 Yes<\/p>\n<p>This triangle is not possible.<\/p>\n<p>(ii) 3 cm, 6 cm, 7 cm<\/p>\n<p>3 + 6 &gt; 7 Yes<\/p>\n<p>6 + 7 &gt; 3 Yes<\/p>\n<p>3 + 7 &gt; 6 Yes<\/p>\n<p>This triangle is possible.<\/p>\n<p>(iii) 6 cm, 3 cm, 2 cm<\/p>\n<p>6 + 3 &gt; 2 Yes<\/p>\n<p>6 + 2 &gt; 3 Yes<\/p>\n<p>2 + 3 &gt; 6 No<\/p>\n<p>This triangle is not possible.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 7 Maths Exercise 6.4<\/p>\n<h6><span class=\"ez-toc-section\" id=\"Question_2Take_any_point_O_in_the_interior_of_a_triangle_PQR_Is\"><\/span><strong>Question 2.<\/strong>Take any point O in the interior of a triangle PQR. Is:<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p><img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/07\/mathematics\/07_math_ncert_ch06_08.png\" \/><\/p>\n<ol>\n<li>OP + OQ &gt; PQ ?<\/li>\n<li>OQ + OR &gt; QR ?<\/li>\n<li>OR + OP &gt; RP ?<\/li>\n<\/ol>\n<p>Since sum of two sides is greater than third side.<\/p>\n<p><strong>Answer:<\/strong><\/p>\n<p>Join OR, OQ and OP.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/07\/mathematics\/07_math_ncert_ch06_16.jpg\" \/><\/p>\n<p>(i) Is OP + OQ &gt; PQ ?<\/p>\n<p>Yes, POQ form a triangle.<\/p>\n<p>(ii) Is OQ + OR &gt; QR ?<\/p>\n<p>Yes, RQO form a triangle.<\/p>\n<p>(iii) Is OR + OP &gt; RP ?<\/p>\n<p>Yes, ROP form a triangle.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 7 Maths Exercise 6.4<\/p>\n<h6><span class=\"ez-toc-section\" id=\"Question_3AM_is_a_median_of_a_triangle_ABC_Is_AB_BC_CA_%3E_2AM\"><\/span><strong>Question 3.<\/strong>AM is a median of a triangle ABC. Is AB + BC + CA &gt; 2AM ?<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p>(Consider the sides of triangles ABM and AMC.)<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/07\/mathematics\/07_math_ncert_ch06_09.jpg\" \/><\/p>\n<p><strong>Answer:<\/strong><\/p>\n<p>Since, the sum of lengths of any two sides in a triangle should be greater than the length of third side.<\/p>\n<p>Therefore, In {tex}\\Delta {\/tex}ABM, AB + BM &gt; AM \u2026\u2026\u2026.(i)<\/p>\n<p>In {tex}\\Delta {\/tex}AMC, AC + MC &gt; AM \u2026\u2026\u2026.(ii)<\/p>\n<p>Adding eq. (i) and (ii),<\/p>\n<p>AB + BM + AC + MC &gt; AM + AM<\/p>\n<p>{tex} \\Rightarrow {\/tex} AB + AC + (BM + MC) &gt; 2AM<\/p>\n<p>{tex} \\Rightarrow {\/tex} AB + AC + BC &gt; 2AM<\/p>\n<p>Hence, it is true.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 7 Maths Exercise 6.4<\/p>\n<h6><span class=\"ez-toc-section\" id=\"Question_4ABCD_is_a_quadrilateral_Is_AB_BC_CD_DA_%3E_AC_BD\"><\/span><strong>Question 4.<\/strong>ABCD is a quadrilateral. Is AB + BC + CD + DA &gt; AC + BD ?<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p><img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/07\/mathematics\/07_math_ncert_ch06_10.jpg\" \/><\/p>\n<p><strong>Answer:<\/strong><\/p>\n<p>Since, the sum of lengths of any two sides in a triangle should be greater than the length of third side.<\/p>\n<p>Therefore, In {tex}\\Delta {\/tex}ABC, AB + BC &gt; AC \u2026\u2026\u2026.(i)<\/p>\n<p>In {tex}\\Delta {\/tex}ADC, AD + DC &gt; AC \u2026\u2026\u2026.(ii)<\/p>\n<p>In {tex}\\Delta {\/tex}DCB, DC + CB &gt; DB \u2026\u2026\u2026.(iii)<\/p>\n<p>In {tex}\\Delta {\/tex}ADB, AD + AB &gt; DB \u2026\u2026\u2026.(iv)<\/p>\n<p>Adding eq. (i), (ii), (iii) and (iv),<\/p>\n<p>AB + BC + AD + DC + DC + CB + AD + AB &gt; AC + AC + DB + DB<\/p>\n<p>{tex} \\Rightarrow {\/tex} (AB + AB) + (BC + BC) + (AD + AD) + (DC + DC) &gt; 2AC + 2DB<\/p>\n<p>{tex} \\Rightarrow {\/tex} 2AB + 2BC + 2AD + 2DC &gt; 2(AC + DB)<\/p>\n<p>{tex} \\Rightarrow {\/tex} 2(AB + BC + AD + DC) &gt; 2(AC + DB)<\/p>\n<p>{tex} \\Rightarrow {\/tex} AB + BC + AD + DC &gt; AC + DB<\/p>\n<p>{tex} \\Rightarrow {\/tex} AB + BC + CD + DA &gt; AC + DB<\/p>\n<p>Hence, it is true.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 7 Maths Exercise 6.4<\/p>\n<p><strong>Question 5.\u00a0<\/strong>ABCD is quadrilateral. Is AB + BC + CD + DA &lt; 2 (AC + BD) ?<\/p>\n<p><strong>Answer:<\/strong><\/p>\n<p>Since, the sum of lengths of any two sides in a triangle should be greater than the length of third side.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/07\/mathematics\/07_math_ncert_ch06_17.png\" \/><\/p>\n<p>Therefore, In {tex}\\Delta {\/tex}AOB, AB &lt; OA + OB \u2026\u2026\u2026.(i)<\/p>\n<p>In {tex}\\Delta {\/tex}BOC, BC &lt; OB + OC \u2026\u2026\u2026.(ii)<\/p>\n<p>In {tex}\\Delta {\/tex}COD, CD &lt; OC + OD \u2026\u2026\u2026.(iii)<\/p>\n<p>In {tex}\\Delta {\/tex}AOD, DA &lt; OD + OA \u2026\u2026\u2026.(iv)<\/p>\n<p>Adding eq. (i), (ii), (iii) and (iv),<\/p>\n<p>AB + BC + CD + DA &lt; OA + OB + OB + OC + OC + OD + OD + OA<\/p>\n<p>{tex} \\Rightarrow {\/tex} AB + BC + CD + DA &lt; 2OA + 2OB + 2OC + 2OD<\/p>\n<p>{tex} \\Rightarrow {\/tex} AB + BC + CD + DA &lt; 2[(AO + OC) + (DO + OB)]\n<p>{tex} \\Rightarrow {\/tex} AB + BC + CD + DA &lt; 2(AC + BD)<\/p>\n<p>Hence, it is proved.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 7 Maths Exercise 6.4<\/p>\n<h6><span class=\"ez-toc-section\" id=\"Question_6The_lengths_of_two_sides_of_a_triangle_are_12_cm_and_15_cm_Between_what_two_measures_should_the_length_of_the_third_side_fall\"><\/span><strong>Question 6.<\/strong>The lengths of two sides of a triangle are 12 cm and 15 cm. Between what two measures should the length of the third side fall?<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p><strong>Answer:<\/strong><\/p>\n<p>Since, the sum of lengths of any two sides in a triangle should be greater than the length of third side.<\/p>\n<p>It is given that two sides of triangle are 12 cm and 15 cm.<\/p>\n<p>Therefore, the third side should be less than 12 + 15 = 27 cm.<\/p>\n<p>And also the third side cannot be less than the difference of the two sides.<\/p>\n<p>Therefore, the third side has to be more than 15 \u2013 12 = 3 cm.<\/p>\n<p>Therefore, the third side could be the length more than 3 cm and less than 27 cm.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_7_Maths_Exercise_64\"><\/span>NCERT Solutions for Class 7 Maths Exercise 6.4<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>NCERT Solutions Class 7 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 7 Maths includes text book solutions from Class 7 Maths Book . NCERT Solutions for CBSE Class 7 Maths have total 15 chapters. 7 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 7 solutions PDF and Maths ncert class 7 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_Students\"><\/span>CBSE app for Students<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To download NCERT Solutions for Class 7 Maths, Social Science Computer Science, Home Science, Hindi English, Maths Science do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through\u00a0<a href=\"https:\/\/play.google.com\/store\/apps\/details?id=in.techchefs.MyCBSEGuide&amp;referrer=utm_source%3Dmycbse_bottom%26utm_medium%3Dtext%26utm_campaign%3Dmycbseads\"><strong>the best app for CBSE students<\/strong><\/a>\u00a0and myCBSEguide website.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions for Class 7 Maths Exercise 6.4 book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 7 Maths chapter wise &#8230; <a title=\"NCERT Solutions for Class 7 Maths Exercise 6.4\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-7-maths-exercise-6-4\/\" aria-label=\"More on NCERT Solutions for Class 7 Maths Exercise 6.4\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":-1,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1388,281],"tags":[283,1535,321,1485,216],"class_list":["post-4307","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics-cbse-class-07","category-ncert-solutions","tag-cbse-study-material","tag-class-7","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 7 Maths Exercise 6.4 | myCBSEguide<\/title>\n<meta name=\"description\" content=\"NCERT Solutions for Class 7 Maths Exercise 6.4 in PDF format for free download. 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