Illustrative Mathematics Grade 8, Unit 1, Lesson 8: Rotation Patterns

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Illustrative Math
Grade 7

Lesson 8: Rotation Patterns

Let’s rotate figures in a plane.

Illustrative Math Unit 8.1, Lesson 8 (printable worksheets)

Lesson 8 Summary

The following diagram shows how to move one part of a figure to another using a rigid transformation.

Lesson 8.1 Building a Quadrilateral

Here is a right isosceles triangle:

1. Rotate triangle ABC 90 degrees clockwise around B.
2. Rotate triangle ABC 180 degrees clockwise around B.
3. Rotate triangle ABC 270 degrees clockwise around B.
4. What would it look like when you rotate the four triangles 90 degrees clockwise around B? 180 degrees? 270 degrees clockwise?

• See Video for Whole Lesson

Lesson 8.2 Rotating a Segment

Create a segment AB and a point C that is not on segment AB. Open Applet

1. Rotate segment AB 180° around point B.
2. Rotate segment AB 180° around point C.
   Construct the midpoint of segment AB with the Midpoint tool.
3. Rotate segment AB 180° around its midpoint. What is the image of A?
4. What happens when you rotate a segment 180°?

Are you ready for more?

Here are two line segments. Is it possible to rotate one line segment to the other? If so, find the center of such a rotation. If not, explain why not.

• Show Answer

  
  

Lesson 8.3 A Pattern of Four Triangles

Here is a diagram built with three different rigid transformations of triangle ABC. Use the applet to answer the questions. It may be helpful to reset the image after each question.
Open Applet

1. Describe a rigid transformation that takes triangle ABC to triangle CDE.
2. Describe a rigid transformation that takes triangle ABC to triangle EFG.
3. Describe a rigid transformation that takes triangle ABC to triangle GHA.
4. Do segments AC, CE, EG, and GA all have the same length? Explain your reasoning.

Lesson 8 Practice Problems

1. For the figure shown here,
   a. Rotate segment CD 180° around point D.
   b. Rotate segment CD 180° around point E.
   c. Rotate segment CD 180° around point M.
2. Here is an isosceles right triangle:
   Draw these three rotations of triangle ABC together.
   a. Rotate triangle ABC 90 degrees clockwise around A.
   b. Rotate triangle ABC 180 degrees around A.
   c. Rotate triangle ABC 270 degrees clockwise around A.
3. Each graph shows two polygons ABCD and A’B’C’D'. In each case, describe a sequence of transformations that takes ABCD to A’B’C’D'.
4. Lin says that she can map Polygon A to Polygon B using only reflections. Do you agree with Lin? Explain your reasoning.

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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