In this lesson, students complete their proofs of the triangle congruence theorems, studying the SideSideSide 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 cooldown, 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.
Lesson overview
 9.1 Warmup: Dare to Be Different (5 minutes)

9.2 Activity: Proving the SideSideSide Triangle Congruence Theorem (15 minutes)
 Includes "Are you Ready for More?" extension problem
 9.3 Activity: What Else Do We Know For Sure About Parallelograms? (15 minutes)
 Lesson Synthesis
 9.4 Cooldown: Practice Seeing Shortcuts (5 minutes)
Learning goals:
 Justify (in writing) the SideSideSide Triangle Congruence Theorem.
 Prove (in writing) opposite angles of a parallelogram are congruent.
Learning goals (student facing):
 Let’s see if we can prove one more set of conditions that guarantee triangles are congruent, and apply theorems.
Learning targets (student facing):
 I can explain why the SideSideSide Triangle Congruence Theorem works.
 I can use the SideSideSide Triangle Congruence Theorem in a proof.
Required materials:
 Dried linguine pasta
 Geometry toolkits
 Protractors
 rulers
Required preparation:
 Provide students with dried linguine pasta if they request it, or tuck it unobtrusively into their geometry toolkits before class.
Standards:
 This lesson builds on the standards: CCSS.7.G.A.2MS.7.G.2CCSS.HSGCO.B.7MS.GCO.7CCSS.HSGCO.B.8MS.GCO.8MO.7.GM.A.2aMO.G.CO.B.6MO.G.CO.B.7
 This lesson builds towards the standards: CCSS.HSGCO.B.8MS.GCO.8CCSS.HSGCO.C.10MS.GCO.10CCSS.HSGCO.C.11MS.GCO.11CCSS.HSGCO.C.9MS.GCO.9MO.G.CO.B.7MO.G.CO.C.9MO.G.CO.C.10MO.G.CO.C.8
IM Algebra 1, Geometry, Algebra 2 is copyright 2019 Illustrative Mathematics and licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.