Illustrative Mathematics Grade 8, Unit 2, Lesson 6: Similarity

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Illustrative Math
Grade 8

Lesson 6: Similarity

Let’s explore similar figures.

Illustrative Math Unit 8.2, Lesson 6 (printable worksheets)

Lesson 6 Summary

The following diagram shows how to use a sequence of transformations to explain why two figures are similar.

Lesson 6.1 Equivalent Expressions

Use what you know about operations and their properties to write three expressions equivalent to the expression shown.

10(2 + 3) - 8 · 3

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Lesson 6.2 Similarity Transformations (Part 1)

1. Triangle EGH and triangle LME are similar. Find a sequence of translations, rotations, reflections, and dilations that shows this.

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2. Hexagon ABCDEF and hexagon HGLKJI are similar. Find a sequence of translations, rotations, reflections, and dilations that shows this.

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Are you ready for more?

The same sequence of transformations takes Triangle A to Triangle B, takes Triangle B to Triangle C, and so on. Describe a sequence of transformations with this property.

Lesson 6.3 Similarity Transformations (Part 2)

Sketch figures similar to Figure A that use only the transformations listed to show similarity.

1. A translation and a reflection. Label your sketch Figure B. Pause here so that your teacher can check your work.
2. A reflection and a dilation with scale factor greater than 1. Label your sketch Figure C.
3. A rotation and a reflection. Label your sketch Figure D.
4. A dilation with scale factor less than 1 and a translation. Label your sketch Figure E.

Lesson 6.4 Methods for Translations and Dilations

Your teacher will give you a set of five cards and your partner a different set of five cards. Using only the cards you were given, find at least one way to show that triangle ABC and triangle DEF are similar. Compare your method with your partner’s method. What is the same about your methods? What is different?

Lesson 6 Practice Problems

1. Each diagram has a pair of figures, one larger than the other. For each pair, show that the two figures are similar by identifying a sequence of translations, rotations, reflections, and dilations that takes the smaller figure to the larger one.
2. Here are two similar polygons.
   Measure the side lengths and angles of each polygon. What do you notice?
3. Each figure shows a pair of similar triangles, one contained in the other. For each pair, describe a point and a scale factor to use for a dilation moving the larger triangle to the smaller one. Use a measurement tool to find the scale factor.

The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.

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