Allen WolmerSandy Springs, Georgia, US,

April 29, 2015

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Teacher Resources

- Mathematics > General
- Mathematics > Geometry

- Grade 9
- Grade 10

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Table of Contents

- Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar
- Students define a similarity transformation as the composition of basic rigid motions and dilations.
- Students know the properties of a similarity transformation are determined by the transformations that compose the similarity transformation
- Students understand that similarity is reflexive, symmetric, and transitive.
- Similar Polygons and Scale Factors

Teacher Resources

Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

Exercises from Illustrative Mathematics

A set of 4 exercises, commentary, and solutions

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Students define a similarity transformation as the composition of basic rigid motions and dilations. Students define two figures to be similar if there is a similarity transformation that takes one to the other.

Students can describe a similarity transformation applied to an arbitrary figure (i.e., not just triangles) and can use similarity to distinguish between figures that resemble each other versus those that are actually similar.

Teacher and Student versions of full lesson from engageNY

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Students know the properties of a similarity transformation are determined by the transformations that compose the similarity transformation.

Students are able to apply a similarity transformation to a figure by construction.

Teacher and Student versions of full lesson from engageNY

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Students understand that similarity is reflexive, symmetric, and transitive.

Students recognize that if two triangles are similar, there is a correspondence such that corresponding pairs of angles have the same measure and corresponding sides are proportional. Conversely, they know that if there is a correspondence satisfying these conditions, then there is a similarity transformation taking one triangle to the other respecting the correspondence.

Teacher and Student versions of full lesson from engageNY

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Similar Polygons and Scale Factors

What if you were told that two pentagons were similar and you were given the lengths of each pentagon's sides. How could you determine the scale factor of pentagon #1 to pentagon #2? After completing this Concept, you'll be able to answer questions like this one about similar polygons.

Lessons, videos, exercises, and text from CK-12.

Additional resources available at this site.

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