Question

AD bisects ∠BAC of ΔABC. Prove that AB > BD.

Answer 1

Given: AD bisects ∠BAC of triangle ABC.

To Prove: AB > BD

ABC is a triangle.

AD is the bisector of ∠BAC.

We have to prove that AB > BD

Since AD is the bisector of ∠BAC

∠BAD = ∠CAD   ...(1)

We know that the exterior angle of a triangle is greater than each of the opposite interior angles.

∠ADB > ∠CAD

From (1), ∠ADB > ∠BAD

We know that in a triangle a side opposite to a greater angle is longer.

The side AB is greater than BD.

Therefore, AB > BD

Hence, proved.