# In triangle side opposite to equal angles are equal

In this chapter we will learn and derive one important concept of geometry.

According to the concept, the sides opposite to equal angles of triangle are equal.

This concept is universal and is applicable for all types of triangle.

You have to remember the concept as it would help to solve variety of geometry related problems.

## Prove that sides opposite to equal angles of triangle are equal

Given:
Given above is triangle ABC in which ∠ABC = ∠ACB = 65 degree

Construction:
Draw line AM which bisect ∠BAC.
Hence, ∠BAM = ∠CAM

To prove:
Side opposite to equal angles are equal.
i.e. AB = AC

Proof
Consider triangle ABM and ACM

∠ABM = ∠ACM = 65 degree
∠BAM = ∠CAM { AM is angle bisector }
AM = MA

By AAS congruency condition, we can say that triangle ABM and ACM are congruent.
i.e. \mathtt{\triangle ABM\ \cong \triangle ACM}

Since both triangle are congruent, we can say that; AB = AC

Hence, we proved that in triangle, sides opposite to equal angles are equal.

Next chapter: Prove that angle opposite to greater side is larger