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Kajal Aggarwal
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Asked: 2020-11-03T10:04:31+00:00 In:

In an isosceles triangle ABC, with AB = AC, the bisectors of Angle B and Angle C intersect each other at O. Join A to O. Show that: (i) OB = OC (ii) AO bisects Angle A

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NCERT Solutions for Class 9 Maths Chapter 7
Important NCERT Questions
Triangles
NCERT Books for Session 2022-2023
CBSE Board and UP Board Others state Board
EXERCISE 7.2
Page No:123
Questions No: 1

2020-2021cbsechapter 7class 9mathematicsncerttriangles
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    2 Answers

    1. Get Hindi Medium and English Medium NCERT Solution for Class 9 Maths to download.
      Please follow the link to visit website for first and second term exams solutions.
      https://www.tiwariacademy.com/ncert-solutions/class-9/maths/chapter-7/

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    2. Best Answer
      In an isosceles triangle ABC, with AB = AC, the bisectors of Angle B and Angle C intersect each other at O. Join A to O. Show that: (i) OB = OC (ii) AO bisects Angle A

      (i) In ABC, AB = AC [∵ Given]
      Hence, ∠ACB = ∠ACB [∵ Angles opposite to equal sides are equal]
      ⇒ (1/2)∠ACB = (1/2)∠ABC
      ⇒ ∠ACO = ∠ABO [∵ OB and OC bisect ∠B and ∠C respectively]
      In ΔABO and ΔACO,
      AB = AC [∵ Given]
      ∠ABO = ∠ACO [∵ Proved above]
      AO = AO [∵ Common]
      Hence, Δ ABO ≅ ΔACO [∵ SAS Congruency Rule]
      OB = OC [∵ CPCT]
      (ii) ΔABO ≅ ΔACO [∵ Proved above]
      ∠BAO = ∠CAO [∵ CPCT]
      Hence, OA bisects angle A.

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