Question

In the adjoining figure, ABC is a triangle in which AD is the bisector of /A. If AD bisect BC, show that triangle ABC is isosceles

Answer 1

In ΔABD and ΔACD

A

D=AD (common side)

B

D=CD (given)

∠ADB=∠ADC (right angle)

So,  

Δ

ABD≅ΔACD

So,  

A B=AC

This proves that ΔABC is isosceles triangle.