# Lesson 7No Bending or Stretching

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

### Learning Targets:

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

## 7.1Measuring 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 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 of a unit.
4. Estimate the length of the segment in the prior question to the nearest 0.1 of a unit.

## 7.2Sides and Angles

1. Translate Polygon so point goes to point . In the image, write in the length of each side, in grid units, next to the side using the draw tool.
2. Rotate Triangle   clockwise using as the center of rotation. In the image, write the measure of each angle in its interior using the draw tool.
3. Reflect Pentagon across line .
1. In the image, write the length of each side, in grid units, next to the side.
2. In the image, write the measure of each angle in the interior.

## 7.3Which One?

Here is a grid showing triangle and two other triangles.

You can use a rigid transformation to take triangle to one of the other triangles.

1. Which one? Explain how you know.

2. Describe a rigid transformation that takes 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 Summary

The transformations we’ve learned about so far, translations, rotations, reflections, and sequences of these motions, are all examples of rigid transformations. A rigid transformation is a move that doesn’t change measurements on any figure.

Earlier, we learned that a figure and its image have corresponding points. With a rigid transformation, figures like polygons also have corresponding sides and corresponding angles. These corresponding parts have the same measurements.

For example, triangle was made by reflecting triangle across a horizontal line, then translating. Corresponding sides have the same lengths, and corresponding angles have the same measures.

measurements in triangle corresponding measurements in image

## Glossary Terms

corresponding

When part of an original figure matches up with part of a copy, we call them corresponding parts. These could be points, segments, angles, or distances.

For example, point in the first triangle corresponds to point in the second triangle.

Segment corresponds to segment .

rigid transformation

A rigid transformation is a move that does not change any measurements of a figure. Translations, rotations, and reflections are rigid transformations, as is any sequence of these.

## 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.

1. Translate the shape so that goes to .
1. Rotate the shape 180 degrees counterclockwise around .
1. Reflect the shape over the line shown.