This lesson is optional, as it goes beyond the scope of the standards. While the standards require only that students prove the Angle-Angle 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 Angle-Side-Angle Triangle Congruence Theorem could be used to prove the Angle-Angle Triangle Similarity Theorem. In this lesson, they see why the Side-Side-Side Triangle Congruence Theorem implies the Side-Side-Side Triangle Similarity Theorem, and why the Side-Angle-Side Triangle Congruence Theorem implies the Side-Angle-Side 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.