The document discusses different methods for proving triangles congruent: 1. SSS (side-side-side) 2. SAS (side-angle-side) 3. ASA (angle-side-angle) 4. AAS (angle-angle-side) 5. HL (hypotenuse-leg) for right triangles only. It also covers built-in information in triangles like shared sides, parallel lines, and vertical angles that can be used for proofs. The document provides examples of congruence proofs using these methods and concepts like corresponding parts of congruent triangles.