This lesson is optional, as it goes beyond the scope of the standards. While the standards only require students to prove the AngleAngle Triangle Similarity Theorem, proving other similarity theorems gives students more opportunities to practice creating viable arguments (MP3). In a previous lesson, students saw how the AngleSideAngle Triangle Congruence Theorem could be used to prove the AngleAngle Triangle Similarity Theorem. In this lesson, they see why the SideSideSide Triangle Congruence Theorem implies the SideSideSide Triangle Similarity Theorem, and why the SideAngleSide Triangle Congruence Theorem implies the SideAngleSide Triangle Similarity Theorem. Students have a chance to use repeated reasoning (MP8) as they apply what worked in one case to additional cases.
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
 10.1 Warmup: Math Talk: Triangle Congruence (5 minutes)
 10.2 Activity: SideAngleSide Triangle Similarity? (15 minutes)

10.3 Activity: SideSideSide Triangle Similarity (15 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 10.4 Cooldown: Make Your Own (5 minutes)
Learning goals:
 Prove the SideAngleSide and SideSideSide Triangle Similarity Theorems (in writing).
Learning goals (student facing):
 Let’s prove more triangles are similar.
Learning targets (student facing):
 I can explain why the SideAngleSide and SideSideSide Triangle Similarity Theorems work.
Standards:
 This lesson builds on the standard: CCSS.HSGCO.B.8MS.GCO.8MO.G.CO.B.7
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