# Lesson 7

No Bending or Stretching

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

### 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 $$\frac18$$ 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 $$\frac18$$ of a unit. 4. Estimate the length of the segment in the prior question to the nearest 0.1 of a unit.

### 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.

2. Rotate Triangle $$B$$ 90 degrees clockwise using $$R$$ as the center of rotation. In the image, write the measure of each angle in its interior using the draw tool.

3. Reflect Pentagon $$C$$ across line $$\ell$$.
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.

### 7.3: Which One?

Here is a grid showing triangle $$ABC$$ and two other triangles.

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.

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?

### 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 $$EFD$$ was made by reflecting triangle $$ABC$$ across a horizontal line, then translating. Corresponding sides have the same lengths, and corresponding angles have the same measures.

measurements in triangle $$ABC$$ corresponding measurements in image $$EFD$$
$$AB = 2.24$$ $$EF = 2.24$$
$$BC = 2.83$$ $$FD = 2.83$$
$$CA = 3.00$$ $$DE = 3.00$$
$$m\angle ABC = 71.6^\circ$$ $$m\angle EFD= 71.6^\circ$$
$$m\angle BCA = 45.0^\circ$$ $$m\angle FDE= 45.0^\circ$$
$$m\angle CAB = 63.4^\circ$$ $$m\angle DEF= 63.4^\circ$$

### Glossary Entries

• 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 $$B$$ in the first triangle corresponds to point $$E$$ in the second triangle. Segment $$AC$$ corresponds to segment $$DF$$.