Basic Properties of Similarity
Videos and solutions to help Grade 8 students learn that similarity is both a symmetric and a transitive relation.
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Lessons for Grade 8
Common Core For Grade 8
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''.
