Question

If the bisector of an angle of a triangle bisects the opposite side, then prove that the triangle is isosceles.

Answer 1

Given :

In $△ABC$, the bisector AD of $\angle A$ bisects the side BC.

To prove :

$AB=AC$

Proof :

In $△ABC$, AD is the bisector of $\angle A$.

$\frac{AB}{AC}=\frac{BD}{DC}$

$\frac{AB}{AC}=1$

$AB=AC$

Therefore, the triangle ABC is isosceles.