Question

In an isosceles triangle ABC , AB = AC, the angle bisectors of angle B and angle C intersect each other at O. Join A to O . Show that 1) OB = OC 2) AO bisects angle A


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Answer 1

➣ Given

⭐AB = AC

⭐∠3 = ∠4

⭐∠5 = ∠6

➣ To prove

⭐∠1 = ∠2

⭐OB = OC

➣ Proof

☯ In ∆ AOB and ∆ AOC

⟹ AO = AO. ( COMMON)

⟹ AB = AC. ( GIVEN).

⟹ ∠B = ∠C ( GIVEN)

☞ OB and OC are the bisectors so

⟹ $\dfrac{1}{2}$∠B = $\dfrac{</strong>1<strong>}{</strong>2<strong>}$∠c

⟹ ∠3 = ∠4

∆ AOB ≌ ∆ AOC by SAS

$\boxed{OB = OC}$ (by cpct)

$\boxed{∠1 = ∠2 }$ (by cpct)

Hope it helps u