# Basic Properties of Similarity

Videos and solutions to help Grade 8 students learn that similarity is both a symmetric and a transitive relation.

## New York State Common Core Math Module 3, Grade 8, Lesson 9

### Lesson 9 Student Outcomes

• Students know that similarity is both a symmetric and a transitive relation.

### Lesson 8 Summary

• Similarity is a symmetric relation. That means that if one figure is similar to another, S ∼ S', then we can be sure that S' ∼ S.
Similarity is a transitive relation. That means that if we are given two similar figures, S ∼ T, and another statement about T ∼ U, then we also know that S ∼ U.

### NYS Math Module 3 Grade 8 Lesson 9

Classwork
Exploratory Challenge 1
The goal is to show that if △ ABC is similar to △ A'B'C', then △ A'B'C' is similar to △ ABC. Symbolically, if △ ABC ∼ △ A'B'C', then △ A'B'C' ∼ △ ABC.

Exploratory Challenge 2
The goal is to show that if △ ABC is similar to △ A'B'C', and △ A'B'C' is similar to △ A'"B'"C'", then is similar to △ ABC is similar to △ A''B''C''. Symbolically, if △ ABC ∼ △ A'B'C', and △ A'B'C' ∼ △ A''B''C'' then △ ABC ∼ △ A''B''C''.