# Unit 4 Congruent Triangles Homework 7 Proofs Review All Methods

In Geometry, understanding and mastering the concept of congruent triangles is essential. In this unit, students will learn and review theorems and postulates related to congruent triangles. Homework 7 is focused on proofs, and this article will review all methods used when proving congruent triangles.

## ASA and AAS Theorems The ASA and AAS theorems provide a way to prove two triangles are congruent. The ASA theorem states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. The AAS theorem states that if two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle, then the two triangles are congruent. Both the ASA and AAS theorems must be used in the proof of congruent triangles.

## SAS Theorem The SAS theorem provides an easier way to prove two triangles are congruent. The SAS theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. This theorem simplifies the proof as it only requires three pieces of congruence information instead of six.

## HL Theorem The HL theorem is a more advanced theorem used to prove congruent triangles. The HL theorem states that if two sides and their included angles of one triangle are congruent to two sides and their included angles of another triangle, then the two triangles are congruent. This theorem requires four pieces of congruence information, making it more difficult to use than the SAS theorem. 