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

  1. Chapter 7 Class 9 Triangles
  2. Serial order wise
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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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