Question

in an isosceles triangle ABC the bisector of Angle B and angle C intersect each other at O then OB bisect a true or false​

Answer 1

$\huge\frak{Answer}$

Refer the attachment.

Answer 2

Given,

AB = AC

∠ABO = ∠OBC

∠ACO =  ∠OBC

To prove,

∠BAO =∠CAO

Solution,

In ΔABC

AB = AC  (given)

∠B = ∠ C  ( angles opposite to equal sides are equal)

1//2 ∠B = 1/2∠C

∠OBC  = ∠OBC

⇒ OB =OC (sides opposite to equal angles are equal)

In ΔAOB and ΔAOC

AB = AC (given)

AO = AO (Common)

∠ABO = ∠ACO (proved above)

ΔAOB≅ΔAOC

∠ BAO = ∠CAO (by CPCT)

⇒AO bisect ∠A.

Hence, proved that AO bisects ∠A