Question

In following figure if AD is the bisector of ∠BAC, then 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 Eq. (i)]

AB > BD [side opposite to greater angle is longer]

Hence proved.