Theorem – Angles opposite to equal sides of an isosceles triangle are equal

Angles opposite to equal sides of an isosceles triangle are equal.

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

To prove: We need to prove that ∠B and ∠C, are equal
                           ∠B = ∠C.

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

Proof:  In △ ABD and △ACD

AB = AC  (Given)

AD =AD (Common)

 ∠BAD = ∠CAD (by construction)

△ ABD ≅  △ACD (by SAS rule)

Thus,  ∠ABD = ∠ACD (Angles are corresponding angles of congruent triangles) So, 

∠B = ∠C

                               Hence proved.

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