Illustrative Mathematics Grade 8, Unit 1, Lesson 12: Congruent Polygons

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Illustrative Math
Grade 8

Lesson 12: Congruent Polygons

Let’s decide if two figures are congruent.

Illustrative Math Unit 8.1, Lesson 12 (printable worksheets)

Lesson 12 Summary

The following diagrams describe how to decide using rigid transformations whether or not two figures are congruent.

Lesson 12.1 Translated Images

All of these triangles are congruent. Sometimes we can take one figure to another with a translation. Shade the triangles that are images of triangle ABC under a translation.

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Lesson 12.2 Congruent Pairs (Part 1)

For each of the following pairs of shapes, decide whether or not they are congruent. Explain your reasoning.

Lesson 12.3 Congruent Pairs (Part 2)

For each pair of shapes, decide whether or not Shape A is congruent to Shape B. Explain how you know.

Are you ready for more?

A polygon has 8 sides: five of length 1, two of length 2, and one of length 3. All sides lie on grid lines. (It may be helpful to use graph paper when working on this problem.)

1. Find a polygon with these properties.
2. Is there a second polygon, not congruent to your first, with these properties?
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Lesson 12 Practice Problems

1. a. Show that the two pentagons are congruent.
   b. Find the side lengths of ABCDE and the angle measures of FGHIJ.
2. For each pair of shapes, decide whether or not the two shapes are congruent. Explain your reasoning.
3. a. Draw segment PQ.
   b. When PQ is rotated 180° around point R, the resulting segment is the same as PQ. Where could point R be located?
4. Here is trapezoid ABCD.
   Using rigid transformations on the trapezoid, build a pattern. Describe some of the rigid transformations you used.

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