# Proving Triangle Congruence with SAS

## What is SAS?

The Side-Angle-Side theorem, or SAS, is a method of proving two triangles are congruent. This theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent. In other words, all corresponding parts of the two triangles are equal.

## Using SAS to Prove Congruence

To prove congruence using SAS, you must first identify the shared angle and two corresponding sides. Then, you must determine if the sides and angle are congruent. This can be done by measuring the angle and sides, or by using the given information (such as the length of the sides and the measure of the angle).

## An Example of Proving Congruence

Let’s take a look at an example. Imagine two triangles ABC and DEF. If the side AB is equal to side DE, the angle BAC is equal to angle EDF, and the side AC is equal to side DF, then we can prove these two triangles are congruent. This is because all three conditions of the SAS theorem are met.

## Conclusion

The Side-Angle-Side theorem is a useful tool for proving two triangles are congruent. By verifying that two sides and the included angle of one triangle are congruent to two sides and the included angle of the other triangle, you can prove the two triangles are congruent. SAS is a valuable tool for solving geometry problems.