Illustrative Mathematics Grade 8, Unit 1, Lesson 11: What Is the Same?

Learning Targets:

  • I can decide visually whether or not two figures are congruent.

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Illustrative Math
Grade 8

Lesson 11: What Is the Same?

Let’s decide whether shapes are the same.

Illustrative Math Unit 8.1, Lesson 11 (printable worksheets)

Lesson 11 Summary

The following diagrams describe how two figures are congruent if one can be lined up exactly with the other by a sequence of rigid transformations.
Congruent Transformation

Lesson 11.1 Find the Right Hands

A person’s hands are mirror images of each other. In the diagram, a left hand is labeled. Shade all of the right hands.

Lesson 11.2 Are They the Same?

For each pair of shapes, decide whether or not they are the same.

Lesson 11.3 Area, Perimeter, and Congruence

  1. Which of these rectangles have the same area as Rectangle R but different perimeter?
  2. Which rectangles have the same perimeter but different area?
  3. Which have the same area and the same perimeter?
  4. Use materials from the geometry tool kit to decide which rectangles are congruent. Shade congruent rectangles with the same color.

Are you ready for more?

In square ABCD, points E, F, G, and H are midpoints of their respective sides. What fraction of square ABCD is shaded? Explain your reasoning.

Lesson 11 Practice Problems

  1. If two rectangles have the same perimeter, do they have to be congruent? Explain how you know.
  2. Draw two rectangles that have the same area, but are not congruent.
  3. For each pair of shapes, decide whether or not it appears that the two shapes are congruent. Explain your reasoning.
  4. a. Reflect Quadrilateral A over the x-axis. Label the image quadrilateral B. Reflect Quadrilateral B over the y-axis. Label the image C.
    b. Are Quadrilaterals A and C congruent? Explain how you know.
  5. The point (-2,-3) is rotated 90 degrees counterclockwise using center (0,0). What are the coordinates of the image?
  6. Describe a rigid transformation that takes Polygon A to Polygon B.

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

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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