Question

Prove that in an isosceles triangle, the angles opposite the equal sides are equal.

Answer 1

Given: $ABC$ is an isosceles triangle in which $AB=AC.$

To prove :- $\angle B=\angle C.$

Construction: Draw an angle bisector of angle $A$ meeting $BC$ at $D.$

Proof :- In $△BAD$ & $△CAD$, we have

$AB=AC$ (Given)

$\angle BAD=\angle CAD$ (By construction)

$AD=AD$ (common)

$△BAD\cong △CAD$ [By SAS congruency rule]

So, $\angle ABD=\angle ACD$ [CPCT]

$\therefore \angle B=\angle C$

Hence, in an isosceles triangle, the angles opposite the equal sides are equal.