Question

In a triangle ABC, AD is the bisector of Angle A. Prove that AB = AC.

Answer 1

If AD is the bisector of ∠A of triangle ABC, show that AB>DB.
Given AD is the bisector of ∠A of triangle ABC
Hence ∠DAB=∠DAC
∠BDA is the exterior angle of the ∆DAC
Hence ∠BDA> ∠DAC
or ∠BDA > ∠DAB Since ∠DAC=∠DAB
→ AB > BD In a triangle sides opposite to greater angle is greater.