# Lesson 8Rotation Patterns

Let’s rotate figures in a plane.

### Learning Targets:

• I can describe how to move one part of a figure to another using a rigid transformation.

Here is a right isosceles triangle:

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

## 8.2Rotating a Segment

Create a segment and a point that is not on segment .

1. Rotate segment around point

2. Rotate segment around point

Construct the midpoint of segment with the Midpoint tool.

1. Rotate segment around its midpoint. What is the image of A?

2. What happens when you rotate a segment ?

### 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.

## 8.3A Pattern of Four Triangles

Here is a diagram built with three different rigid transformations of triangle .

Use the applet to answer the questions. It may be helpful to reset the image after each question.

1. Describe a rigid transformation that takes triangle to triangle .
2. Describe a rigid transformation that takes triangle to triangle .
3. Describe a rigid transformation that takes triangle to triangle .
4. Do segments , , , and  all have the same length? Explain your reasoning.

## Lesson 8 Summary

When we apply a 180-degree rotation to a line segment, there are several possible outcomes:

• The segment maps to itself (if the center of rotation is the midpoint of the segment).
• The image of the segment overlaps with the segment and lies on the same line (if the center of rotation is a point on the segment).
• The image of the segment does not overlap with the segment (if the center of rotation is not on the segment).

We can also build patterns by rotating a shape. For example, triangle shown here has . If we rotate triangle 60 degrees, 120 degrees, 180 degrees, 240 degrees, and 300 degrees clockwise, we can build a hexagon.

## Lesson 8 Practice Problems

1. For the figure shown here,

1. Rotate segment around point .
2. Rotate segment around point .
3. Rotate segment around point .
2. Here is an isosceles right triangle:

Draw these three rotations of triangle together.

1. Rotate triangle 90 degrees clockwise around .
2. Rotate triangle 180 degrees around .
3. Rotate triangle 270 degrees clockwise around .
3. Each graph shows two polygons and . In each case, describe a sequence of transformations that takes to .

4. Lin says that she can map Polygon A to Polygon B using only reflections. Do you agree with Lin? Explain your reasoning.