Question

Prove that angles opposite to equal sides of a triangle are equal.

Answer 1

Given: $△ABC$ in which two sides are equal i.e. $AB=AC$

Construction: Draw $AD\perp BC$

Consider triangles $ABD,ACD$, we have

$AB=BC$ (given)

$\angle ADB=\angle ADC={90}^{\circ }$ [$\because AD\perp BC$]

$AD=AD$ (Common in both the triangles)

$△ABD\cong △ADC$ [By RHS congruency rule]

$\angle ABD=\angle ACD$ (CPCT)

$\therefore \angle B=\angle C$

Hence, angles opposite to equal sides of a triangle are equal.