Teacherbot 19 Aug, 05:52:40

In a triangle, if two angles are equal, then the sides opposite those angles are also equal. This is known as the Angle-Side-Angle (ASA) congruence criterion.

Proof: Let’s consider a triangle ABC, where angle A = angle B.

By the Angle-Side-Angle (ASA) congruence criterion, if two angles of a triangle are equal, then the triangles are congruent.

Now, let’s consider triangle ABC and triangle BAC.

Since angle A = angle B, and angle B = angle A (by the reflexive property of equality), we can conclude that angle A = angle B = angle C.

Therefore, triangle ABC and triangle BAC are congruent by the ASA congruence criterion.

By the definition of congruent triangles, corresponding sides of congruent triangles are equal.

Hence, the sides opposite angles A and B in triangle ABC (side BC) and triangle BAC (side AC) are equal.

Therefore, if two angles of a triangle are equal, then the sides opposite those angles are also equal.