Illustrative Mathematics Grade 8, Unit 1, Lesson 13: Congruence

Learning Targets:

  • I can use distances between points to decide if two figures are congruent.

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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?

Lesson 13.3 Corresponding Points in Congruent Figures

Here are two congruent shapes with some corresponding points labeled.

  1. Draw the points corresponding to B, D, and E, and label them B', D', and E'.
  2. 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?
  3. 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

  1. Which of these four figures are congruent to the top figure?
  2. 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.
  3. Here are two figures.
    Show, using measurement, that these two figures are not congruent.
  4. 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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