This document discusses two postulates for proving triangles congruent: 1. Angle-Side-Angle (ASA) postulate - If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. 2. Angle-Angle-Side (AAS) postulate - If two angles and one non-included side of one triangle are congruent to two angles and the non-included side of another triangle, then the triangles are congruent. The document provides examples of applying these postulates to determine if pairs of triangles are congruent. It also notes there are no AAA or SSA postulates to prove triangles congruent.