{"id":8683,"date":"2022-02-15T22:12:15","date_gmt":"2022-02-15T16:42:15","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=8683"},"modified":"2025-05-28T16:42:01","modified_gmt":"2025-05-28T11:12:01","slug":"ncert-solutions-for-class-7-maths-chapter-7-congruence-of-triangles-ex-7-2","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-material\/ncert-solutions-for-class-7\/maths\/chapter-7\/congruence-of-triangles\/ex-7-2\/","title":{"rendered":"NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.2"},"content":{"rendered":"<h2>NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.2<\/h2>\n<ul>\n<li><\/li>\n<\/ul>\n<p><strong>NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Exercise 7.2<\/strong><br \/>\nEx 7.2 Class 7 Maths Question 1.<br \/>\nWhich congruence criterion do you use in the following?<br \/>\n(a) Given:<br \/>\nAC = DF<br \/>\nAB = DE<br \/>\nBC = EF<br \/>\nSo, \u2206ABC = \u2206DEF<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-73807\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/NCERT-Solutions-for-Class-7-Maths-Chapter-7-Congruence-Ex-7.2-1.png\" alt=\"NCERT Solutions for Class 7 Maths Chapter 7 Congruence Ex 7.2 1\" width=\"266\" height=\"105\" \/><br \/>\n(b) Given:<br \/>\nZX = RP<br \/>\nRQ = ZY<br \/>\n\u2220PRQ = \u2220XZY<br \/>\nSo, \u2206PQR \u2245 \u2206XYZ<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-73808\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/NCERT-Solutions-for-Class-7-Maths-Chapter-7-Congruence-Ex-7.2-2.png\" alt=\"NCERT Solutions for Class 7 Maths Chapter 7 Congruence Ex 7.2 2\" width=\"308\" height=\"129\" \/><br \/>\n(c) Given: \u2220MLN = \u2220FGH<br \/>\n\u2220NML = \u2220GFH<br \/>\nML = FG<br \/>\nSo, \u2206LMN = \u2206GFH<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-73809\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/NCERT-Solutions-for-Class-7-Maths-Chapter-7-Congruence-Ex-7.2-3.png\" alt=\"NCERT Solutions for Class 7 Maths Chapter 7 Congruence Ex 7.2 3\" width=\"327\" height=\"101\" \/><br \/>\n(d) Given:<br \/>\nEB = DB<br \/>\nAE = BC<br \/>\n\u2220A = \u2220C = 90\u00b0<br \/>\n\u2206ABE = \u2206CDB<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-73810\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/NCERT-Solutions-for-Class-7-Maths-Chapter-7-Congruence-Ex-7.2-4.png\" alt=\"NCERT Solutions for Class 7 Maths Chapter 7 Congruence Ex 7.2 4\" width=\"243\" height=\"115\" \/><br \/>\nSolution:<br \/>\n(a) \u2206ABC \u2245 \u2206DEF (BY SSS rule)<br \/>\n(b) \u2206PQR \u2245 \u2206XYZ (BY SAS rule)<br \/>\n(c) \u2206LMN \u2245 \u2206GFH (BY ASA rule)<br \/>\n(d) \u2206ABE \u2245 \u2206CDB (BY RHS rule)<\/p>\n<p>Ex 7.2 Class 7 Maths Question 2.<br \/>\nYou want to show that \u2206ART = \u2206PEN,<br \/>\n(a) If you have to use SSS criterion, then you need to show<br \/>\n(i) AR =<br \/>\n(ii) RT =<br \/>\n(iii) AT =<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-73814\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/NCERT-Solutions-for-Class-7-Maths-Chapter-7-Congruence-Ex-7.2-5.png\" alt=\"NCERT Solutions for Class 7 Maths Chapter 7 Congruence Ex 7.2 5\" width=\"359\" height=\"95\" \/><br \/>\n(b) If it is given that \u2220T = \u2220N and you are to use SAS criterion, you need to have<br \/>\n(i) RT = and<br \/>\n(ii) PN =<br \/>\n(c) If it is given that AT = PN and you are to use ASA criterion, you need to have<br \/>\n(i) ZA<br \/>\n(ii) ZT<br \/>\nSolution:<br \/>\n(a) For SSS criterion, we need<br \/>\n(i) AR = PE<br \/>\n(ii) RT = EN<br \/>\n(iii) AT = PN<br \/>\n(b) For SAS criterion, we need<br \/>\n(i) RT = EN and<br \/>\n(ii) PN = AT<br \/>\n(c) For ASA criterion, we need<br \/>\n(i) \u2220A = \u2220P<br \/>\n(ii) \u2220T = \u2220N<\/p>\n<p>Ex 7.2 Class 7 Maths Question 3.<br \/>\nYou have to show that \u2206AMP \u2245 \u2206AMQ. In the fallowing proof, supply the missing reasons.<\/p>\n<table border=\"2\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" colspan=\"2\" width=\"154\"><strong>Steps<\/strong><\/td>\n<td style=\"text-align: center;\" width=\"134\"><strong>Reasons<\/strong><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\" width=\"154\">(i) PM = QM<\/td>\n<td width=\"134\">(i)<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\" width=\"154\">(ii) \u2220PMA \u2013 \u2220QMA<\/td>\n<td width=\"134\">(ii)<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\" width=\"154\">(iii) AM = AM<\/td>\n<td width=\"134\">(iii)<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\" width=\"154\">(iv) \u2206AMP = \u2206AMQ<\/td>\n<td width=\"134\">(iv)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-73816\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/NCERT-Solutions-for-Class-7-Maths-Chapter-7-Congruence-Ex-7.2-6.png\" alt=\"NCERT Solutions for Class 7 Maths Chapter 7 Congruence Ex 7.2 6\" width=\"176\" height=\"135\" \/><\/p>\n<p>Solution:<\/p>\n<table border=\"2\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" colspan=\"2\" width=\"154\"><strong>Steps<\/strong><\/td>\n<td style=\"text-align: center;\" width=\"134\"><strong>Reasons<\/strong><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\" width=\"154\">(i) PM = QM<\/td>\n<td width=\"134\">(i) Given<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\" width=\"154\">(ii) \u2220PMA = \u2220QMA<\/td>\n<td width=\"134\">(ii) Given<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\" width=\"154\">(iii) AM = AM<\/td>\n<td width=\"134\">(iii) Common<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\" width=\"154\">(iv) \u2206AMP = \u2206AMQ<\/td>\n<td width=\"134\">(iv) SAS rule<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Ex 7.2 Class 7 Maths Question 4.<br \/>\nIn \u2206ABC, \u2220A = 30\u00b0, \u2220B = 40\u00b0 and \u2220C = 110\u00b0<br \/>\nIn \u2206PQR, \u2220P = 30\u00b0, \u2220Q = 40\u00b0 and \u2220R = 110\u00b0.<br \/>\nA student says that \u2206ABC = \u2206PQR by AAA congruence criterion. Is he justified? Why or why not?<br \/>\nSolution:<br \/>\nThe student is not justified because there is not criterion for AAA congruence rule.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-73817\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/NCERT-Solutions-for-Class-7-Maths-Chapter-7-Congruence-Ex-7.2-7.png\" alt=\"NCERT Solutions for Class 7 Maths Chapter 7 Congruence Ex 7.2 7\" width=\"306\" height=\"149\" \/><br \/>\nExample: In \u2206ABC and \u2206PQR, we have \u2220A = 30\u00b0, \u2220B = 40\u00b0, \u2220C = 110\u00b0<br \/>\n\u2220P = 30\u00b0, \u2220Q = 40\u00b0, \u2220R = 110\u00b0<br \/>\nBut \u2206ABC is not congruent to \u2206PQR.<\/p>\n<p>Ex 7.2 Class 7 Maths Question 5.<br \/>\nIn the figure, the two triangles are congruent. The corresponding parts are marked. We can write \u2206RAT \u2245 ?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-73818\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/NCERT-Solutions-for-Class-7-Maths-Chapter-7-Congruence-Ex-7.2-8.png\" alt=\"NCERT Solutions for Class 7 Maths Chapter 7 Congruence Ex 7.2 8\" width=\"290\" height=\"101\" \/><br \/>\nSolution:<br \/>\nIn \u2206RAT and \u2206WON<br \/>\n\\(\\overline{\\mathrm{AT}}=\\overline{\\mathrm{ON}}\\) (Given)<br \/>\n\\(\\overline{\\mathrm{AR}}=\\overline{\\mathrm{OW}}\\) (Given)<br \/>\n\u2220A = \u2220O (Given)<br \/>\n\u2234 \u2206RAT \u2245 \u2206WON (By SAS rule)<\/p>\n<p>Ex 7.2 Class 7 Maths Question 6.<br \/>\nComplete the congruence statement:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-73819\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/NCERT-Solutions-for-Class-7-Maths-Chapter-7-Congruence-Ex-7.2-9.png\" alt=\"NCERT Solutions for Class 7 Maths Chapter 7 Congruence Ex 7.2 9\" width=\"333\" height=\"147\" \/><br \/>\nSolution:<br \/>\nRefer to Fig. (i)<br \/>\nIn \u2206BCA and \u2206BTA<br \/>\n\u2220C = \u2220T (Given)<br \/>\n\\(\\overline{\\mathrm{BC}}=\\overline{\\mathrm{BT}}\\) (Given)<br \/>\n\u2220BA = \u2220TBA (Given)<br \/>\n\u2234 \u2206BCA = \u2206BTA (by ADA rule)<br \/>\nRefer to Fig. (ii)<br \/>\nIn \u2206QRS and \u2206TPQ<br \/>\n\\(\\overline{\\mathrm{RS}}=\\overline{\\mathrm{PQ}}\\) (Given)<br \/>\n\\(\\overline{\\mathrm{QS}}=\\overline{\\mathrm{TQ}}\\) (Given)<br \/>\n\u2220RSQ = \u2220PQT (Given)<br \/>\n\u2234 \u2206QRS = \u2206TPQ (by SAS rule)<\/p>\n<p>Ex 7.2 Class 7 Maths Question 7.<br \/>\nIn a squared sheet, draw two triangles of equal areas such that:<br \/>\n(i) the triangles are congruent.<br \/>\n(ii) the triangle are not congruent.<br \/>\nWhat can you say about their perimeters?<br \/>\nSolution:<br \/>\n(i) On the given square sheet, we have draw two congruent triangles i.e.<br \/>\n\u2206ABC = \u2206DEF<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-73821\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/NCERT-Solutions-for-Class-7-Maths-Chapter-7-Congruence-Ex-7.2-10-1.png\" alt=\"NCERT Solutions for Class 7 Maths Chapter 7 Congruence Ex 7.2 10\" width=\"233\" height=\"237\" \/><br \/>\nsuch that<br \/>\n\\(\\overline{\\mathrm{AB}}=\\overline{\\mathrm{DE}}, \\overline{\\mathrm{BC}}=\\overline{\\mathrm{EF}} \\text { and } \\overline{\\mathrm{AC}}=\\overline{\\mathrm{DF}}\\)<br \/>\nOn adding, we get<br \/>\n\\(\\overline{\\mathrm{AB}}+\\overrightarrow{\\mathrm{BC}}+\\overrightarrow{\\mathrm{AC}}=\\overline{\\mathrm{DE}}+\\overline{\\mathrm{EF}}+\\overline{\\mathrm{DF}}\\)<br \/>\ni.e. perimeters of \u2206ABC = Perimeter of \u2206DEF<\/p>\n<p>(ii) On the other square sheet, we have drawn two triangles ABC and PQR which are not congruent.<br \/>\nSuch that<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-73822\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/NCERT-Solutions-for-Class-7-Maths-Chapter-7-Congruence-Ex-7.2-11.png\" alt=\"NCERT Solutions for Class 7 Maths Chapter 7 Congruence Ex 7.2 11\" width=\"261\" height=\"248\" \/><br \/>\nAdding both sides, we get<br \/>\n\\(\\overline{\\mathrm{AB}}+\\overline{\\mathrm{BC}}+\\overline{\\mathrm{AC}} \\neq \\overline{\\mathrm{PQ}}+\\overline{\\mathrm{QR}}+\\overline{\\mathrm{PR}}\\)<br \/>\ni.e., perimeter of \u2206ABC \u2260 the perimeter of \u2206PQR.<\/p>\n<p>Ex 7.2 Class 7 Maths Question 8.<br \/>\nDraw a rough sketch of two triangles, such that they have five pairs of congruent parts but still<br \/>\nthe triangles are not congruent.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-73823\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/NCERT-Solutions-for-Class-7-Maths-Chapter-7-Congruence-Ex-7.2-12.png\" alt=\"NCERT Solutions for Class 7 Maths Chapter 7 Congruence Ex 7.2 12\" width=\"335\" height=\"115\" \/><br \/>\nSolution:<br \/>\nWe have \u2206PQR and \u2206TSU<br \/>\n\\(\\overline{\\mathrm{PQ}}=\\overline{\\mathrm{SU}}\\) (Given)<br \/>\n\\(\\overline{\\mathrm{PR}}=\\overline{\\mathrm{ST}}\\) (Given)<br \/>\n\u2220Q = \u2220S (Given)<br \/>\n\u2220P = \u2220T (Given)<br \/>\n\u2220R = \u2220U (Given)<br \/>\nSince non of the criteria of congruence is relevant here.<br \/>\n\u2234 \u2206PQR and \u2206TSU are not congruent.<\/p>\n<p>Ex 7.2 Class 7 Maths Question 9.<br \/>\nIf \u2206ABC and \u2206PQR are to be congruent, name one additional pair of corresponding parts. What criterion did you use?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-73824\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/NCERT-Solutions-for-Class-7-Maths-Chapter-7-Congruence-Ex-7.2-13.png\" alt=\"NCERT Solutions for Class 7 Maths Chapter 7 Congruence Ex 7.2 13\" width=\"257\" height=\"147\" \/><br \/>\nSolution:<br \/>\nIn \u2206ABC and \u2206PQR<br \/>\n\u2220B = \u2220Q (Given)<br \/>\n\u2220C = \u2220R (Given)<br \/>\nFor \u2206ABC = \u2206PQR<br \/>\nBC must equal to \\(\\overline{Q R}\\) criterion that we used is ASA rule.<br \/>\nHence, the additional pair of corresponding part is \\(\\overline{\\mathrm{BC}}=\\overline{\\mathrm{QR}}\\).<\/p>\n<p>Ex 7.2 Class 7 Maths Question 10.<br \/>\nExplain, why \u2206ABC = \u2206FED<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-73825\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/NCERT-Solutions-for-Class-7-Maths-Chapter-7-Congruence-Ex-7.2-14.png\" alt=\"NCERT Solutions for Class 7 Maths Chapter 7 Congruence Ex 7.2 14\" width=\"282\" height=\"101\" \/><br \/>\nSolution:<br \/>\nIn \u2206ABC and \u2206FED<br \/>\n\u2220B = \u2220E = 90\u00b0 (Given)<br \/>\n\u2220A = \u2220F (Given)<br \/>\n\u2234 \u2220A + \u2220B = \u2220E + \u2220F<br \/>\n180\u00b0 \u2013 \u2220C = 180\u00b0 \u2013 \u2220D<br \/>\n[Angle sum property of triangles]\n\u2234 \u2220C =\u2220D<br \/>\nBC = ED (Given)<br \/>\n\u2234 \u2206ABC = \u2206FED (By ASA rule)<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-107725\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/NCERT-Solutions-for-Class-7-Maths-Chapter-7-Congruence-of-Triangles-Ex-7.2-Q1.png\" alt=\"NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.2 Q1\" width=\"666\" height=\"661\" \/><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-107724\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/NCERT-Solutions-for-Class-7-Maths-Chapter-7-Congruence-of-Triangles-Ex-7.2-Q1.1.png\" alt=\"NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.2 Q1.1\" width=\"774\" height=\"593\" \/><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-107726\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/NCERT-Solutions-for-Class-7-Maths-Chapter-7-Congruence-of-Triangles-Ex-7.2-Q2.png\" alt=\"NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.2 Q2\" width=\"631\" height=\"651\" \/><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-107728\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/NCERT-Solutions-for-Class-7-Maths-Chapter-7-Congruence-of-Triangles-Ex-7.2-Q3.png\" alt=\"NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.2 Q3\" width=\"759\" height=\"600\" \/><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-107729\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/NCERT-Solutions-for-Class-7-Maths-Chapter-7-Congruence-of-Triangles-Ex-7.2-Q4.png\" alt=\"NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.2 Q4\" width=\"631\" height=\"686\" \/><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-107730\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/NCERT-Solutions-for-Class-7-Maths-Chapter-7-Congruence-of-Triangles-Ex-7.2-Q5.png\" alt=\"NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.2 Q5\" width=\"761\" height=\"560\" \/><\/p>\n<p><strong>Question 8.<\/strong><br \/>\nDraw a rough sketch of two triangles such that they have five pairs of congruent parts but still the triangles are not congruent.<br \/>\n<strong>Solution:<\/strong><br \/>\nIn some special cases (which depend on the lengths of the sides and the size of the angle involved),<\/p>\n<p>SSA is enough to show congruence. However, it is not always enough. Consider the following triangles :<\/p>\n<p>Here side AB is congruent to side DE (S) side AC is congruent to side DF(S) angle C is congruent to angle F(A)<\/p>\n<p>But the triangles are not congruent, as we can see.<\/p>\n<p><strong>What happens is this :<\/strong> If we draw a vertical line through point A in the first triangle, we can sort of \u201cflip\u201d side AB around this line to get the second triangle. If we were to lay one triangle on top of the other and draw the vertical line, this how it would look.<\/p>\n<p>Clearly, side DE is just side AB flipped around the line. So, we have not changed the length of the side, and the other side AC (or DF) is unchanged, as is angle C (or F). So, these two triangles that have the same SSA information, but they are not congruent.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-107732\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/NCERT-Solutions-for-Class-7-Maths-Chapter-7-Congruence-of-Triangles-Ex-7.2-Q9.png\" alt=\"NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.2 Q9\" width=\"760\" height=\"695\" \/><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.2 NCERT Solutions for Class 7 Maths Chapter [&hellip;]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Get NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.2 at infinity learn.","custom_permalink":"study-material\/ncert-solutions-for-class-7\/maths\/chapter-7\/congruence-of-triangles\/ex-7-2\/"},"categories":[13,19,21],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - 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