This document discusses different postulates for proving that two triangles are congruent, including: side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), and angle-angle-side (AAS). It provides examples of applying each postulate to determine if two triangles are congruent and identifies that there are no angle-angle-angle (AAA) or side-side-angle (SSA) postulates. The document also has exercises for the reader to practice using the postulates to determine if pairs of triangles are congruent.