The side opposite to equal angles of a triangle are equal

The side opposite to equal angles of a triangle are equal.

Given: A triangle △ ABC in which angles opposite to sides AC and AB of are ∠B and ∠C, and  ∠B = ∠C.

To prove: We need to prove that sides AB and AC, are equal
                           AB = AC.

Construction: Draw the bisector of ∠A, and let D be the point of intersection of this bisector.

Proof:  In △ ABD and △ ACD

 ∠B = ∠C  (Given)

AD =AD (Common)

 ∠BAD = ∠CAD (by construction)

△ ABD ≅  △ACD (by ASA congruence rule)

Thus,  AB = AC (Sides of corresponding angles of congruent triangles)

So, AB = AC (Corresponding parts of congruent triangles)

Hence proved.

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