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 study diagrams and try to identify which triangle congruence theorem applies. Each diagram they study is drawn from a proof of an important result, preparing students for later work 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.
- Justify (in writing) the Side-Side-Side Triangle Congruence Theorem.
- Prove (in writing) opposite angles of a parallelogram are congruent.
- Let’s see if we can prove one more set of conditions that guarantee triangles are congruent, and apply theorems.
Provide students with dried linguine pasta if they request it, or tuck it unobtrusively into their geometry toolkits before class.
- I can explain why the Side-Side-Side Triangle Congruence Theorem works.
- I can use the Side-Side-Side Triangle Congruence Theorem in a proof.
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