{"id":4429,"date":"2020-09-09T06:09:11","date_gmt":"2020-09-09T00:39:11","guid":{"rendered":"https:\/\/kseebsolutions.guru\/?p=4429"},"modified":"2021-07-02T15:03:37","modified_gmt":"2021-07-02T09:33:37","slug":"kseeb-solutions-class-8-maths-chapter-11-ex-11-5","status":"publish","type":"post","link":"https:\/\/kseebsolutions.guru\/kseeb-solutions-class-8-maths-chapter-11-ex-11-5\/","title":{"rendered":"KSEEB Solutions for Class 8 Maths Chapter 11 Congruency of Triangles Ex 11.5"},"content":{"rendered":"

Students can Download Maths Chapter 11 Congruency of Triangles Ex 11.5 Questions and Answers, Notes Pdf, KSEEB Solutions for Class 8 Maths<\/a> helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.<\/p>\n

Karnataka Board Class 8 Maths Chapter 11 Congruency of Triangles Ex 11.5<\/h2>\n

Question 1.
\nIn \u2206 ABC, AC = AB and the altitude AD bisects BC prove that \u2206 ADC = \u2206 ADB.
\n\"KSEEB
\nAnswer:
\nIn \u2206 ABD and \u2206 ACD
\nAB = AC [data]
\nBD = DC [data]
\nAD = AD [Common side]
\n\u2234 \u2206 ABD = \u2206 ACD [SSS postulate].<\/p>\n

Question 2.
\nIn a square PQRS, diagonals bisect each other at O. Prove that: \u2206 POQ = \u2206 QOR = \u2206 ROS = \u2206 SOP
\n\"KSEEB
\nAnswer:
\n\u2206 POQ and \u2206 QOR
\nPQ = QR [Sides of a square]
\nPO = OR [data]
\nOQ = OQ [Common side]
\n\u2234 \u2206 POQ = \u2206 QOR [SSS postulate] \u2026i In AQOR and AROS QR = RS [Sides of a square]
\nQO = OS [data]
\nOR = OR [Common side]
\n\u2234 \u2206 QOR = \u2206 ROS [SSS postulate] \u2026ii
\nIn \u2206ROS and \u2206SOP
\nSR = SP [Sides of a square]
\nRO = OP [data]
\nOS = OS [Common side]
\n\u2234 \u2206 ROS \u2245 \u2206SOP [SSSpostulate]\u2026iii
\nFrom (i), (ii) and (iii)
\n\u2206POQ \u2245 \u2206QOR \u2245 \u2206ROS \u2245 \u2206SOP<\/p>\n

Question 3.
\nIn figure two sides AB, BC, and the median AD of \u2206ABC are respectively equal to two sides PQ, QR, and median PS of \u2206PQR. Prove that
\n(1) AADB \u2245 APSQ
\n(2) AADC \u2245 APSR
\nDoes if follow that triangles ABC and PQR are congruent.
\n\"KSEEB
\nAns
\n1. IN \u2206 ADB and \u2206 PSQ
\nAB = PQ [data]
\nBD = QS [BC = QR, D and S are the mid points]
\nAD = PS [data]
\n\u2206 ABD \u2245 \u2206PQR [SSS postulate]
\n\u2220APB = \u2220 PSQ [Corresponding sides]<\/p>\n

2. \u2206 ADC and \u2206 PSR
\nAB = PQ [data]
\nDC = SR
\n[BC = QR, D and S are the mid points]
\n\u2220ADC =\u2220PSR
\n\u2234[\u2220ADC = 180 – \u2220APB
\n\u2220PSR = 180 -\u2220PSQ
\n\u2220ADB =\u2220PSQ]
\n\u2206 ABC \u2245 \u2206 PSR [SAS postulate]
\nYes from the results of (i) and( ii)
\n\u2206 ABC = \u2206 PQR<\/p>\n

Question 4.
\nIn \u2206 PQR, PQ = QR, L, M, and N are the midpoint of the sides of PQ, QR, and RP respectively prove that LN = MN
\n\"KSEEB
\nAnswer:
\nPQ = QR [data]
\n\u2220P = \u2220R [Theorem l]
\nIn \u2206 PLN and RMN
\nPL = RM
\n[PQ = QR and L and M are the midpoints]
\n\u2220P = \u2220R
\nPN = NR [N is the mid point of PR]
\n\u2234 \u2206 PLN \u2245 \u2206RMN [SAS postulate]
\n\u2234 LN = MN [Corresponding sides]<\/p>\n","protected":false},"excerpt":{"rendered":"

Students can Download Maths Chapter 11 Congruency of Triangles Ex 11.5 Questions and Answers, Notes Pdf, KSEEB Solutions for Class 8 Maths helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations. Karnataka Board Class 8 Maths Chapter 11 Congruency of Triangles Ex 11.5 Question 1. In \u2206 …<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/4429"}],"collection":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/comments?post=4429"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/4429\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=4429"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=4429"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=4429"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}