Question 1 (ii)
In an isosceles triangle ABC, with AB = AC, the bisectors of $∠ B a n d ∠ C$ intersect each other at O. Join A to O. Show that:
AO bisects $∠ A$

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Solution

$I t i s g i v e n t h a t A B = A C t h e r e f o r e, ∠ B = ∠ C (A n g l e s o p p o s i t e t o e q u a l s i d e s a r e e q u a l) \Rightarrow \frac{1}{2} (∠ B) = \frac{1}{2} (∠ C) \Rightarrow ∠ O B C = ∠ O C B (O B a n d O C a r e b i s e c t o r s o f ∠ B a n d a n d ∠ C) T h e r e f o r e, O B = O C (S i d e s o p p o s i t e t o e q u a l a n g l e s a r e e q u a l)$
$I n Δ A O B a n d Δ A O C O B = O C (P r o v e d a b o v e) A B = A C (G i v e n) A O = A O (C o m m o n) ∴ Δ A O B ≅ Δ A O C (B y S S S c o n g r u e n c e r u l e) S o, ∠ B A O = ∠ C A O (C o r r e s p o n d i n g p a r t s o f c o n g r u e n t t r i a n g l e s a r e e q u a l) \Rightarrow A O b i s e c t s ∠ A .$

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Properties of Isosceles Triangle

Standard IX Mathematics

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Question 1 (ii) 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: AO bisects ∠ A

Question 1 (ii)
In an isosceles triangle ABC, with AB = AC, the bisectors of $∠ B a n d ∠ C$ intersect each other at O. Join A to O. Show that:
AO bisects $∠ A$