{"id":1928,"date":"2022-11-04T08:29:24","date_gmt":"2022-11-04T08:29:24","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=1928"},"modified":"2022-11-04T08:29:24","modified_gmt":"2022-11-04T08:29:24","slug":"ncert-solutions-class-7-maths-chapter-6-the-triangle-and-its-properties-ex-6-4","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-7-maths-chapter-6-the-triangle-and-its-properties-ex-6-4\/","title":{"rendered":"NCERT Solutions Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.4"},"content":{"rendered":"<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">NCERT Solutions Class 7 Mathematics\u00a0<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Chapter &#8211; 6 (The Triangle and its Properties)<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">The NCERT Solutions in English Language for Class 7 Mathematics <strong>Chapter &#8211; 6 The Triangle and its Properties <\/strong>Exercise 6.4 has been provided here to help the students in solving the questions from this exercise.\u00a0<\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Chapter : 6 The Triangles and its Properties<\/strong><\/span><\/p>\n<ul>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-7-maths-chapter-6-the-triangle-and-its-properties-ex-6-1\" target=\"_blank\" rel=\"noopener\"><span style=\"font-family: georgia, palatino, serif;\">NCERT Solution Class 7 Maths Exercise &#8211; 6.1<\/span><\/a><\/span><\/li>\n<li><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-7-maths-chapter-6-the-triangle-and-its-properties-ex-6-2\" target=\"_blank\" rel=\"noopener\"><span style=\"font-family: georgia, palatino, serif;\">NCERT Solution Class 7 Maths Exercise &#8211; 6.2<\/span><\/a><\/span><\/span><\/li>\n<li><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-7-maths-chapter-6-the-triangle-and-its-properties-ex-6-3\" target=\"_blank\" rel=\"noopener\"><span style=\"font-family: georgia, palatino, serif;\">NCERT Solution Class 7 Maths Exercise &#8211; 6.3<\/span><\/a><\/span><\/span><\/li>\n<li><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-7-maths-chapter-6-the-triangle-and-its-properties-ex-6-5\" target=\"_blank\" rel=\"noopener\"><span style=\"font-family: georgia, palatino, serif;\">NCERT Solution Class 7 Maths Exercise &#8211; 6.5<\/span><\/a><\/span><\/span><\/li>\n<\/ul>\n<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Exercise &#8211; 6.4\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>1. Is it possible to have a triangle with the following sides?<br \/>\n<\/strong><strong>(i) 2 cm, 3 cm, 5 cm<br \/>\n(ii) 3 cm, 6 cm, 7 cm<br \/>\n(iii) 6 cm, 3 cm, 2 cm<br \/>\n<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<br \/>\n(i) 2 cm, 3 cm, 5 cm<br \/>\n<\/strong>Sum of the two sides = 2 cm + 3 cm = 5 cm Third side = 5 cm<br \/>\nWe have, Sum of any two sides = the third side i.e. 5 cm = 5 cm<br \/>\nHence, the triangle is not possible.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) 3 cm, 6 cm, 7 cm<br \/>\n<\/strong>Sum of the two sides = 3 cm + 6 cm = 9 cm Third side = 7 cm<br \/>\nWe have sum of any two sides &gt; the third<br \/>\nside. i.e. 9 cm &gt; 7 cm<br \/>\nHence, the triangle is possible.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iii) 6 cm, 3 cm, 2 cm<br \/>\n<\/strong>Sum of the two sides = 3 cm + 2 cm \u2013 5 cm Third side = 6 cm<br \/>\nWe have, sum of any two sides &lt; the third sid6 i.e. 5 cm &lt; 6 cm Hence, the triangle is not possible.<br \/>\n<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>2. Take any point O in the interior of a triangle PQR. Is<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1978 alignright\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-6.4-Q2i.png\" alt=\"NCERT Class 7 Maths Solution\" width=\"235\" height=\"106\" \/><br \/>\n<\/strong><strong>(i) OP + OQ &gt; PQ?<br \/>\n<\/strong><strong>(ii) OQ + OR &gt; QR?<br \/>\n<\/strong><strong>(iii) OR + OP &gt; RP?<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<br \/>\n<\/strong>If we take any point O in the interior of a triangle PQR and join OR, OP, OQ.<br \/>\nThen, we get three triangles \u0394OPQ, \u0394OQR and \u0394ORP is shown in the figure below.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1979\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-6.4-Ans2i.png\" alt=\"NCERT Class 7 Maths Solution\" width=\"232\" height=\"113\" \/><br \/>\nThe sum of the length of any two sides is always greater than the third side.<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(i) OP + OQ &gt; PQ?<br \/>\n<\/strong>Yes, In \u2206OPQ, we have<\/span><br \/>\n<span style=\"color: #000000;\">OP + OQ &gt; PQ<\/span><br \/>\n<span style=\"color: #000000;\">[Sum of any two sides of a triangle is greater than the third side]<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(ii) OQ + OR &gt; QR?<br \/>\n<\/strong>Yes, In \u2206OQR, we have OQ + OR &gt; QR<\/span><br \/>\n<span style=\"color: #000000;\">[Sum of any two sides of a triangle is greater than the third side]<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(iii) OR + OP &gt; RP?<br \/>\n<\/strong>Yes, In \u2206OPR, we have OR + OP &gt; RP<\/span><br \/>\n<span style=\"color: #000000;\">[Sum of any two sides of a triangle is greater than the third side]<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>3. AM is a median of a triangle ABC.<br \/>\n<\/strong><strong>Is AB + BC + CA &gt; 2 AM?<br \/>\n<\/strong><strong>(Consider the sides of triangles \u0394ABM and \u0394AMC.)<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1980\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-6.4-Q3.png\" alt=\"NCERT Class 7 Maths Solution\" width=\"239\" height=\"140\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<br \/>\n<\/strong>We know that,<br \/>\nThe sum of the length of any two sides is always greater than the third side.<br \/>\nNow consider the \u0394ABM,<br \/>\nHere, AB + BM &gt; AM &#8212;&#8212;&#8212;&#8211; [equation (i)]<br \/>\nThen, consider the \u0394ACM<br \/>\nHere, AC + CM &gt; AM &#8212;&#8212;&#8212;&#8211;\u00a0 [equation (ii)]<br \/>\nBy adding equation (i) and (ii) we get,<br \/>\nAB + BM + AC + CM &gt; AM + AM<br \/>\nFrom the figure we have, BC = BM + CM<br \/>\nAB + BC + AC &gt; 2 AM<br \/>\nHence, the given expression is true.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>4. ABCD is a quadrilateral.<br \/>\n<\/strong><strong>Is AB + BC + CD + DA &gt; AC + BD?<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1981\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-6.4-Q4.png\" alt=\"NCERT Class 7 Maths Solution\" width=\"177\" height=\"102\" \/><br \/>\n<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<br \/>\n<\/strong>We know that,<br \/>\nThe sum of the length of any two sides is always greater than the third side.<br \/>\nNow consider the \u0394ABC,<br \/>\nHere, AB + BC &gt; CA\u00a0 \u00a0 \u00a0 &#8212;&#8212;&#8212;- [equation (i)]<br \/>\nThen, consider the \u0394BCD<br \/>\nHere, BC + CD &gt; DB\u00a0 \u00a0 \u00a0 &#8212;&#8212;&#8212;- [equation (ii)]<br \/>\nConsider the \u0394CDA<br \/>\nHere, CD + DA &gt; AC\u00a0 \u00a0 \u00a0 &#8212;&#8212;&#8212;- [equation (iii)]<br \/>\nConsider the \u0394DAB<br \/>\nHere, DA + AB &gt; DB \u00a0 \u00a0 \u00a0 &#8212;&#8212;&#8212;- [equation (iv)]<br \/>\nBy adding equation (i), (ii), (iii) and (iv) we get,<br \/>\nAB + BC + BC + CD + CD + DA + DA + AB &gt; CA + DB + AC + DB<br \/>\n2AB + 2BC + 2CD + 2DA &gt; 2CA + 2DB<br \/>\nTake out 2 on both the side,<br \/>\n2(AB + BC + CA + DA) &gt; 2(CA + DB)<br \/>\nAB + BC + CA + DA &gt; CA + DB<br \/>\nHence, the given expression is true.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>5. ABCD is quadrilateral. Is AB + BC + CD + DA &lt; 2 (AC + BD)<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<br \/>\n<\/strong>Let us consider ABCD is quadrilateral and P is the point where the diagonals are intersect. As shown in the figure below.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1982\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-6.4-Q5.png\" alt=\"NCERT Class 7 Maths Solution\" width=\"184\" height=\"101\" \/><br \/>\nWe know that,<br \/>\nThe sum of the length of any two sides is always greater than the third side.<br \/>\nNow consider the \u0394PAB,<br \/>\nHere, PA + PB &gt; AB \u00a0 \u00a0 \u00a0 &#8212;&#8212;&#8212;- [equation (i)]<br \/>\nThen, consider the \u0394PBC<br \/>\nHere, PB + PC &gt; BC \u00a0 \u00a0 \u00a0 &#8212;&#8212;&#8212;- [equation (ii)]<br \/>\nConsider the \u0394PCD<br \/>\nHere, PC + PD &gt; CD \u00a0 \u00a0 \u00a0 &#8212;&#8212;&#8212;- [equation (iii)]<br \/>\nConsider the \u0394PDA<br \/>\nHere, PD + PA &gt; DA \u00a0 \u00a0 \u00a0 &#8212;&#8212;&#8212;- [equation (iv)]<br \/>\nBy adding equation (i), (ii), (iii) and (iv) we get,<br \/>\nPA + PB + PB + PC + PC + PD + PD + PA\u00a0&gt; AB + BC + CD + DA<br \/>\n2PA + 2PB + 2PC + 2PD\u00a0&gt; AB + BC + CD + DA<br \/>\n2PA + 2PC + 2PB + 2PD\u00a0&gt; AB + BC + CD + DA<br \/>\n2(PA + PC) + 2(PB + PD)\u00a0&gt; AB + BC + CD + DA<br \/>\nFrom the figure we have, AC = PA + PC and BD = PB + PD<br \/>\nThen,<br \/>\n2AC + 2BD\u00a0&gt; AB + BC + CD + DA<br \/>\n2(AC + BD)\u00a0&gt; AB + BC + CD + DA<br \/>\nHence, the given expression is true.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>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?<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<br \/>\n<\/strong>We know that,<br \/>\nThe sum of the length of any two sides is always greater than the third side.<br \/>\nFrom the question, it is given that two sides of triangle are 12 cm and 15 cm.<br \/>\nSo, the third side length should be less than the sum of other two sides,<br \/>\n12 + 15 = 27 cm.<br \/>\nThen, it is given that the third side is cannot not be less than the difference of the two sides, 15 \u2013 12 = 3 cm<br \/>\nSo, the length of the third side falls between 3 cm and 27 cm.<\/span><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions Class 7 Mathematics\u00a0 Chapter &#8211; 6 (The Triangle and its Properties) The NCERT Solutions in English Language for Class 7 Mathematics Chapter &#8211; 6 The Triangle and its Properties Exercise 6.4 has been provided here to help the students in solving the questions from this exercise.\u00a0 Chapter : 6 The Triangles and its [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[219],"tags":[296,297,283,5],"class_list":["post-1928","post","type-post","status-publish","format-standard","hentry","category-class-7-maths","tag-ncert-class-7-maths-chapter-6-the-triangle-and-its-properties-in-english","tag-ncert-solutions-class-7-maths-chapter-6-in-english","tag-ncert-solutions-class-7-maths-in-english","tag-ncert-solutions-in-english"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.9 (Yoast SEO v27.4) - 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