Sir please help me to solve the ncert class 9th solution of chapter triangles.How I solve this question of exercise 7.2 question number 1. Find the simplest and easiest solution of this question , also give me the best solution of this question. In an isosceles triangle ABC, with AB = AC, the bisectors of B and C intersect each other at O. Join A to O. Show that: (i) OB = OC (ii) AO bisects A.
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In an isosceles triangle ABC, with AB = AC, the bisectors of B and C intersect each other at O. Join A to O. Show that: (i) OB = OC (ii) AO bisects A. Q.1
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Solution:
Given:
AB = AC and
the bisectors of B and C intersect each other at O
(i) Since ABC is an isosceles with AB = AC,
B = C
½ B = ½ C
⇒ OBC = OCB (Angle bisectors)
∴ OB = OC (Side opposite to the equal angles are equal.)
(ii) In ΔAOB and ΔAOC,
AB = AC (Given in the question)
AO = AO (Common arm)
OB = OC (As Proved Already)
So, ΔAOB ΔAOC by SSS congruence condition.
BAO = CAO (by CPCT)
Thus, AO bisects A.