Lesson 10
Other Conditions for Triangle Similarity
Lesson Narrative
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.
Learning Goals
Teacher Facing
 Prove the SideAngleSide and SideSideSide Triangle Similarity Theorems (in writing).
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.
CCSS Standards
Building On
Glossary Entries

similar
One figure is similar to another if there is a sequence of rigid motions and dilations that takes the first figure onto the second.
Triangle \(A'B'C'\) is similar to triangle \(ABC\) because a rotation with center \(B\) followed by a dilation with center \(P\) takes \(ABC\) to \(A'B'C'\).