Question

Prove that if two angles of a triangle are equal, then opposite sides to them are also equal.

Answer 1

Given :

A $△ABC$ in which $\angle B=\angle C$.

To prove :

$AB=AC$

Construction :

Draw the bisector of $\angle A$ and let it meet BC at D.

Proof :

In $△s$ ABD and ACD,

$\angle B=\angle C$

$\angle BAD=\angle CAD$

$AD=AD$

So, by AAS criterion of congruence,

$△ABD\cong △ACD$

$⟹AB=AC$