Question

In the following figure, AD is the bisector of ∠BAC. Prove that AB > BD.

Answer 1

Given: ABC is a triangle such that AD is the bisector of ∠BAC.

To prove: AB > BD.

Proof: Since, AD is the bisector of ∠BAC.

But ∠BAD = CAD   ...(i)

∴ ∠ADB > ∠CAD   ...[Exterior angle of a triangle is greater than each of the opposite interior angle]

∴ ∠ADB > ∠BAD   ...[From equation (i)]

AB > BD  ...[Side opposite to greater angle is longer]

Hence proved.