Ex 7.2, 1 - In an isosceles triangle ABC, with AB = AC - Ex 7.2

Ex 7.2, 1 - Chapter 7 Class 9 Triangles - Part 2

Ex 7.2, 1 - Chapter 7 Class 9 Triangles - Part 3

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Transcript

Ex 7.2,1 In an isosceles triangle ABC, with AB = AC the bisectors of ∠𝐡 and ∠C interest each other at O . Join A to O. show that : OB = OC Given: AB = AC OB is the bisector of ∠B So, βˆ π΄π΅π‘‚ = βˆ π‘‚π΅πΆ = 1/2 ∠𝐡 OC is the bisector of ∠C So, βˆ π΄πΆπ‘‚ = βˆ π‘‚πΆπ΅ = 1/2 ∠𝐢 To prove: OB = OC Proof: Since, AB = AC β‡’ ∠ACB = ∠ABC 1/2∠ACB = 1/2∠ABC βˆ π‘‚πΆπ΅ = βˆ π‘‚π΅πΆ Hence, OB = OC Hence proved Ex 7.2,1 In an isosceles triangle ABC, with AB = AC the bisectors of ∠𝐡 and ∠𝐴 interest each other at O . Join A to O. show that : (ii) AO bisects ∠𝐴. To prove: ∠OAB= ∠OAC From part (i) OB = OC …(1) Also, In βˆ†ABO and βˆ†ACO, we have AB = AC AO = AO OB = OC ∴ βˆ† ABO β‰… βˆ† ACO β‡’ βˆ π‘‚π΄π΅ = ∠OAC Hence proved

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.