{"id":4417,"date":"2020-09-09T05:56:34","date_gmt":"2020-09-09T00:26:34","guid":{"rendered":"https:\/\/kseebsolutions.guru\/?p=4417"},"modified":"2021-07-02T15:03:37","modified_gmt":"2021-07-02T09:33:37","slug":"kseeb-solutions-class-8-maths-chapter-11-ex-11-4","status":"publish","type":"post","link":"https:\/\/kseebsolutions.guru\/kseeb-solutions-class-8-maths-chapter-11-ex-11-4\/","title":{"rendered":"KSEEB Solutions for Class 8 Maths Chapter 11 Congruency of Triangles Ex 11.4"},"content":{"rendered":"

Students can Download Maths Chapter 11 Congruency of Triangles Ex 11.4 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 11.4<\/h2>\n

Question 1.
\nIn the given figure. If AB || DC and P is the midpoint of BD prove that P is also the midpoint of BD prove that p is also the midpoint of AC.
\n\"KSEEB
\nAnswer:
\nIn \u2206 PDC and \u2206 PAB
\nPD = PB (data)
\n\u2220DPC = \u2220APB [V.O.A]
\n\u2220PD\u2206 = \u2220PBA [Alternate angles AB || CD]
\n\u2234 \u2206 PDC \u2245 \u2206 PAB [ASA postulate]
\n\u2234 PC = PA [Corresponding sides]
\n\u2234 P is the midpoint AC<\/p>\n

Question 2.
\nIn the adjacent figure, CD and BE are altitudes of an isosceles triangle ABC with AC = AB prove that AE = AD.
\n\"KSEEB
\nAnswer:
\nIn \u2206ADC and \u2206AEB
\nAC = AB [data]
\n\u2220ADC = \u2220AEB[BE & CD altitudes]
\n\u2220DAC =\u2220EAB [Common angle]
\n\u2206 ADC = \u2206 AEB[AS\u2206postulate]
\nAD = AE [Corresponding sides]<\/p>\n

Question 3.
\nIn the figure, AP and BQ are perpendiculars to the line segment AB and AP = BQ. Prove that O is the midpoint of line segment AB as well as PQ.
\n\"KSEEB
\nAnswer:
\nIn \u2206APO and \u2206BQO
\nAP = BQ [data]
\n\u2220POA = \u2220BOQ [ V.O.A]
\n\u2220PAO = \u2220QBO = 90\u00b0
\n[AP & BQ are perpendiculars]
\n\u2234 \u2206APO = \u2206BQO [AS\u2206 postulate]
\n\u2234 AO = BO [Corresponding sides]
\nPO = OQ
\n\u2234 O is the midpoint of AB and PQ.<\/p>\n

Question 4.
\nSuppose ABC is an isosceles triangle with AB = AC, BD and CE are bisectors of|fi andlC. Prove that BD = CE.
\n\"KSEEB
\nAns.
\nIn \u2206ABD and \u2206ACE
\n\u2220BAD = \u2220CAE [Common angle]
\nAB = AC [data]
\n\u2220ABD = \u2220ACE [\u2220B =\u2220C and BD and CE are anglar bisectors]
\n\u2234 \u2206 ABD \u2245 \u2206 ACE [AS\u2206 postulate]
\nBD = CE [Corresponding sides]<\/p>\n

Question 5.
\nSuppose ABC is an equiangular triangle. Prove that it is equilateral. (You have seen earlier that an equilateral triangle is equiangular. Thus for triangles equiangularity is equivalent is equilaterality.
\n\"KSEEB
\nAnswer:
\nABC is an equiangular triangle i.e.,
\n\u2220A =\u2220B =\u2220C
\n\u2220A = \u2220B
\nBC = AC \u2026(I) [Theorem2]
\n\u2220A =\u2220C
\n\u2234BC = AB \u2026.(I) [Theorem2]
\nFrom (i) and (ii)
\nAB = BC = AC
\n\u2234 \u2206ABC is equilateral.<\/p>\n","protected":false},"excerpt":{"rendered":"

Students can Download Maths Chapter 11 Congruency of Triangles Ex 11.4 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 11.4 Question 1. In the …<\/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\/4417"}],"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=4417"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/4417\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=4417"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=4417"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=4417"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}