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 provides examples of using these methods to determine if pairs of triangles are congruent or not. It also discusses using corresponding parts of congruent triangles (CPCTC) to prove additional parts are congruent if two triangles are already shown to be congruent.