Question

In triangle ABC if AD is bisector of angle A show that AB>BD and AC > DC

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.
In the same manner, we can prove that AC> DC