In this lesson, students complete their proofs of the triangle congruence theorems, studying the Side-Side-Side Triangle Congruence Theorem. They then have the opportunity to apply the theorem to a proof about parallelograms. Students continue to work on writing clear proofs. Students convince a partner and then a skeptic of their proof that opposite angles in a parallelogram are congruent (MP3). The second skill that is introduced in this lesson is looking for structure in order to decide which triangle congruence theorem applies in a particular proof (MP7). In the Cool-down, students have an opportunity to identify which triangle congruence theorem applies to given diagrams. Each diagram they study is drawn from a proof of an important result, preparing students for later work of proving theorems about triangles, parallelograms, and lines.

Technology isn’t required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.