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Illustrative Math

Grade 8

#### Lesson 13: Congruence

Let’s find ways to test congruence of interesting figures.

Illustrative Math Unit 8.1, Lesson 13 (printable worksheets)

#### Lesson 13 Summary

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

#### Lesson 13.1 Not Just the Vertices

Trapezoids ABCD and A’B’C’D' are congruent.

- Draw and label the points on A’B’C’D' that correspond to E and F.
- Draw and label the points on ABCD that correspond to G' and H'.
- Draw and label at least three more pairs of corresponding points.

#### Lesson 13.2 Congruent Ovals

Are any of the ovals congruent to one another? Explain how you know.

#### Are you ready for more?

You can use 12 toothpicks to create a polygon with an area of five square toothpicks, like this:
Can you use exactly 12 toothpicks to create a polygon with an area of four square toothpicks?

Here are two congruent shapes with some corresponding points labeled.

- Draw the points corresponding to B, D, and E, and label them B', D', and E'.
- Draw line segments AD and A’D' and measure them. Do the same for segments BC and B’C' and for segments AE and A’E'. What do you notice?
- Do you think there could be a pair of corresponding segments with different lengths? Explain.

#### Lesson 13.4 Astonished Faces

Here are two faces, Max and Frankie. Are these faces congruent? Explain your reasoning.

#### Lesson 13 Practice Problems

- Which of these four figures are congruent to the top figure?
- These two figures are congruent, with corresponding points marked.

a. Are angles ABC and A’B’C' congruent? Explain your reasoning.

b. Measure angles ABC and A’B’C' to check your answer.
- Here are two figures.

Show, using measurement, that these two figures are not congruent.
- Each picture shows two polygons, one labeled Polygon A and one labeled Polygon B. Describe how to move Polygon A into the position of Polygon B using a transformation.

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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