In Figure, AD is the bisector of ∠ BAC. Prove that AB BD.

Question

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

Philoid · Accepted Answer

Given: AD is the bisector of ∠BAC.

As AD is the bisector of ∠BAC.

∠BAD = ∠CAD …(1)

∠ADB > ∠CAD (exterior angle of a triangle is greater than each of opposite interior angle)

Then ∠ADB > ∠BAD (from (1))

⇒ AB > BD (opposite sides to greater angle is greater)

Hence proved.