{"id":42954,"date":"2022-05-25T06:00:39","date_gmt":"2022-05-25T00:30:39","guid":{"rendered":"https:\/\/cbselibrary.com\/?p=42954"},"modified":"2023-11-10T10:01:25","modified_gmt":"2023-11-10T04:31:25","slug":"ml-aggarwal-class-7-solutions-for-icse-maths-chapter-12-check-your-progress","status":"publish","type":"post","link":"https:\/\/cbselibrary.com\/ml-aggarwal-class-7-solutions-for-icse-maths-chapter-12-check-your-progress\/","title":{"rendered":"ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Check Your Progress"},"content":{"rendered":"<h2>ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Check Your Progress<\/h2>\n<p>Question 1.<br \/>\nState, giving reasons, whether the following pairs of triangles are congruent or not:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-81594\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-7-Solutions-for-ICSE-Maths-Chapter-12-Congruence-of-Triangles-Check-Your-Progress-Q1.1.png\" alt=\"ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Check Your Progress Q1.1\" width=\"495\" height=\"459\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-7-Solutions-for-ICSE-Maths-Chapter-12-Congruence-of-Triangles-Check-Your-Progress-Q1.1.png 495w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-7-Solutions-for-ICSE-Maths-Chapter-12-Congruence-of-Triangles-Check-Your-Progress-Q1.1-300x278.png 300w\" sizes=\"(max-width: 495px) 100vw, 495px\" \/><br \/>\nSolution:<br \/>\n(i) In the given figure, using the SSS criterion triangles one congruent.<br \/>\n(ii) Triangles are congruent for the criterion ASA criterion.<br \/>\n(iii) Triangles are congruent for the criterion RHS.<br \/>\n(iv) In the first triangle, third angle = 180\u00b0 &#8211; (70\u00b0 + 50\u00b0) = 180\u00b0 &#8211; 120\u00b0 = 60\u00b0<br \/>\nNow triangles are congruent for ASA criterion.<br \/>\n(v) Not congruent as included angles of the given two sides are not equal.<br \/>\n(vi) Not congruent as the included sides are different.<\/p>\n<p>Question 2.<br \/>\nGiven below are measurements of some parts of two triangles. Examine whether the two triangles are congruent or not. In case of congruence, give reasons and write in symbolic form:<\/p>\n<table border=\"2\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" width=\"222\"><strong>\u2206ABC<\/strong><\/td>\n<td style=\"text-align: center;\" width=\"222\"><strong>\u2206PQR<\/strong><\/td>\n<\/tr>\n<tr>\n<td width=\"222\">(i) AB = 4 cm, BC = 5 cm, \u2220B = 70\u00b0<\/td>\n<td width=\"222\">(i) QR = 4 cm, RP = 5 cm, \u2220R = 70\u00b0<\/td>\n<\/tr>\n<tr>\n<td width=\"222\">(ii) AB = 4 cm, BC = 5 cm, \u2220B = 80\u00b0<\/td>\n<td width=\"222\">(ii) PQ = 4 cm, RP = 5 cm, \u2220R = 80\u00b0<\/td>\n<\/tr>\n<tr>\n<td width=\"222\">(iii) BC = 6 cm, \u2220A = 90\u00b0, \u2220C = 50\u00b0<\/td>\n<td width=\"222\">(iii) QR = 6 cm, \u2220R = 50\u00b0, ZQ = 40\u00b0<\/td>\n<\/tr>\n<tr>\n<td width=\"222\">(iv) AB = 5 cm, \u2220A = 90\u00b0, BC = 8 cm<\/td>\n<td width=\"222\">(iv) PR = 5 cm, \u2220P = 90\u00b0, QR = 8 cm<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-81595\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-7-Solutions-for-ICSE-Maths-Chapter-12-Congruence-of-Triangles-Check-Your-Progress-Q2.1.png\" alt=\"ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Check Your Progress Q2.1\" width=\"300\" height=\"163\" \/><br \/>\nSolution:<br \/>\n(i) In \u2206ABC and \u2206PQR<br \/>\nAB = QR = 4 cm<br \/>\nBC = RP = 5 cm<br \/>\n\u2220B = \u2220R = 70\u00b0<br \/>\n\u2206ABC = \u2206PQR (SAS criterion)<br \/>\n(ii) In \u2206ABC and \u2206PQR<br \/>\nAB = PQ = 4 cm<br \/>\nBC = RP = 5 cm not corresponding sides<br \/>\n\u2220B = \u2220R = 80\u00b0 not corresponding angles<br \/>\nTriangles are not congruent.<br \/>\n(iii) BC = QR = 6 cm<br \/>\n\u2220A = \u2220P = 90\u00b0 (Third angle)<br \/>\n\u2220C = \u2220R = 50\u00b0<br \/>\nTriangles are congruent for ASA criterion.<br \/>\n(iv) AB = PR = 5 cm (Side)<br \/>\n\u2220A = \u2220P = 90\u00b0<br \/>\nBC = QR = 8 cm (Hypotenuse)<br \/>\nTriangles are congruent for RHS criterion.<\/p>\n<p>Question 3.<br \/>\nIn the given figure, ABC is an isosceles triangle with AB = AC and AD is one of its altitudes.<br \/>\n(i) State the three pairs of equal parts in \u2206ADB and \u2206ADC.<br \/>\n(zz) Is \u2206ADB = \u2206ADC? Give reasons.<br \/>\n(iii) Is \u2220B = \u2220C? Why?<br \/>\n(iv) Is BD = DC? Why?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-81596\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-7-Solutions-for-ICSE-Maths-Chapter-12-Congruence-of-Triangles-Check-Your-Progress-Q3.1.png\" alt=\"ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Check Your Progress Q3.1\" width=\"148\" height=\"178\" \/><br \/>\nSolution:<br \/>\n\u2206ABC is an isosceles triangle with AB = AC<br \/>\nand AD is one of the altitudes.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-81597\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-7-Solutions-for-ICSE-Maths-Chapter-12-Congruence-of-Triangles-Check-Your-Progress-Q3.2.png\" alt=\"ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Check Your Progress Q3.2\" width=\"147\" height=\"172\" \/><br \/>\n(i) In \u2206ADB and \u2206ADC<br \/>\nSide AD = AD (Common)<br \/>\nHypotenuse, AB = AC (Given)<br \/>\n\u2220ADB = \u2220ADC = 90\u00b0 (\u2235 AB \u22a5 BC)<br \/>\n\u2206ADB = \u2206ADC<br \/>\n\u2220B = \u2220C (c.p.c.t)<br \/>\nand BD = CD (c.p.c.t)<\/p>\n<p>Question 4.<br \/>\nIn the given figure, OA bisects \u2220A and \u2220ABO = \u2220OCA. Prove that OB = OC.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-81598\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-7-Solutions-for-ICSE-Maths-Chapter-12-Congruence-of-Triangles-Check-Your-Progress-Q4.1.png\" alt=\"ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Check Your Progress Q4.1\" width=\"166\" height=\"163\" \/><br \/>\nSolution:<br \/>\nIn \u2206OAB and \u2206OAC<br \/>\n\u2220OAB = \u2220OAC (\u2235 OA bisects \u2220A)<br \/>\n\u2220ABO = \u2220ACO (Given)<br \/>\nOA = OA (common)<br \/>\n\u2206OAB = \u2206OAC (AAS congruence rule)<br \/>\nOB = OC (Corresponding parts of congruent As)<\/p>\n<p>Question 5.<br \/>\nIn the given figure , prove that<br \/>\n(i) AB = FC<br \/>\n(ii) AF = BC.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-81599\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2019\/06\/ML-Aggarwal-Class-7-Solutions-for-ICSE-Maths-Chapter-12-Congruence-of-Triangles-Check-Your-Progress-Q5.1.png\" alt=\"ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Check Your Progress Q5.1\" width=\"242\" height=\"218\" \/><br \/>\nSolution:<br \/>\nIn \u2206ABE and \u2206DFC<br \/>\n\u2220B = \u2220F (each 90\u00b0)<br \/>\nAE = DC (Given)<br \/>\nBE = DF (Given)<br \/>\n\u2206ABE = \u2206DFC (RHS congruence rule)<br \/>\n(i) AB = FC (Corresponding parts of congruent \u2206s)<br \/>\n(ii) As AB = FC (Proved above)<br \/>\n\u21d2 AF + FB = FB + BC<br \/>\n\u21d2 AF + FB &#8211; FB = BC<br \/>\n\u21d2 AF = BC<\/p>\n<h4><a href=\"https:\/\/cbselibrary.com\/ml-aggarwal-icse-solutions-for-class-7-maths\/\">ML Aggarwal Class 7 Solutions for ICSE Maths<\/a><\/h4>\n","protected":false},"excerpt":{"rendered":"<p>ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Check Your Progress Question 1. State, giving reasons, whether the following pairs of triangles are congruent or not: Solution: (i) In the given figure, using the SSS criterion triangles one congruent. (ii) Triangles are congruent for the criterion ASA criterion. (iii) Triangles &#8230; <a title=\"ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Check Your Progress\" class=\"read-more\" href=\"https:\/\/cbselibrary.com\/ml-aggarwal-class-7-solutions-for-icse-maths-chapter-12-check-your-progress\/\" aria-label=\"More on ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Check Your Progress\">Read more<\/a><\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[3034],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.8 (Yoast SEO v18.4.1) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Check Your Progress - CBSE Library<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/cbselibrary.com\/ml-aggarwal-class-7-solutions-for-icse-maths-chapter-12-check-your-progress\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Check Your Progress\" \/>\n<meta property=\"og:description\" content=\"ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Check Your Progress Question 1. 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State, giving reasons, whether the following pairs of triangles are congruent or not: Solution: (i) In the given figure, using the SSS criterion triangles one congruent. (ii) Triangles are congruent for the criterion ASA criterion. (iii) Triangles ... 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