# Illustrative Mathematics Grade 8, Unit 1, Lesson 7: No Bending or Stretching

Learning Targets:

• I can describe the effects of a rigid transformation on the lengths and angles in a polygon.

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Illustrative Math

#### Lesson 7: No Bending or Stretching

Let’s compare measurements before and after translations, rotations, and reflections.

Illustrative Math Unit 8.1, Lesson 7 (printable worksheets)

#### Lesson 7 Summary

The following diagram shows the effects of a rigid transformation on the lengths and angles in a polygon..

#### Lesson 7.1 Measuring Segments

For each question, the unit is represented by the large tick marks with whole numbers.

1. Find the length of this segment to the nearest 1/8 of a unit.
2. Find the length of this segment to the nearest 0.1 of a unit.
3. Estimate the length of this segment to the nearest 1/8 of a unit.
4. Estimate the length of the segment in the prior question to the nearest 0.1 of a unit.

#### Lesson 7.2 Sides and Angles

1. Translate Polygon A so point P goes to point P'. In the image, write in the length of each side, in grid units, next to the side using the draw tool.
Open Applet
2. Rotate Triangle B, 90° clockwise using R as the center of rotation. In the image, write the measure of each angle in its interior using the draw tool.
Open Applet
3. Reflect Pentagon C across line l.
a. In the image, write the length of each side, in grid units, next to the side.
b. In the image, write the measure of each angle in the interior.
Open Applet

#### Lesson 7.3 Which One?

Here is a grid showing triangle ABC and two other triangles.
Open Applet
You can use a rigid transformation to take triangle ABC to one of the other triangles.

1. Which one? Explain how you know.
2. Describe a rigid transformation that takes ABC to the triangle you selected.

#### Are you ready for more?

A square is made up of an L-shaped region and three transformations of the region. If the perimeter of the square is 40 units, what is the perimeter of each L-shaped region?

#### Lesson 7 Practice Problems

1. Is there a rigid transformation taking Rhombus P to Rhombus Q? Explain how you know.
2. Describe a rigid transformation that takes Triangle A to Triangle B.
3. Is there a rigid transformation taking Rectangle A to Rectangle B? Explain how you know.
4. For each shape, draw its image after performing the transformation. If you get stuck, consider using tracing paper.
a. Translate the shape so that A goes to A'.
b. Rotate the shape 180 degrees counterclockwise around B.

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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