# Prove that, if the bisector of ∠BAC of ΔABC is perpendicular to side BC, then ΔABC is an isosceles triangle.

Given: Bisector of BAC of ΔABC is perpendicular to side BC

To Prove: ΔABC is an isosceles triangle.

Proof:

In ΔABD and ΔACD

Since, AD is the angle Bisector of ΔABC

So, by ASA congruency test

ΔABD ΔACD

Therefore,

AB = AC ………………. corresponding sides of congruent triangles.

ABD = ACD ……………… corresponding angles of congruent triangles.

ABC = ACB

Since, AB = AC and ABC = ACB so, ΔABC is an isosceles triangle.

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