# Lesson 9

Moves in Parallel

Let’s transform some lines.

### Problem 1

1. Draw parallel lines $$AB$$ and $$CD$$.
2. Pick any point $$E$$. Rotate $$AB$$ 90 degrees clockwise around $$E$$.
3. Rotate line $$CD$$ 90 degrees clockwise around $$E$$.
4. What do you notice?

### Problem 2

Use the diagram to find the measures of each angle. Explain your reasoning.

1. $$m{\angle ABC}$$
2. $$m{\angle EBD}$$
3. $$m{\angle ABE}$$

### Problem 3

Points $$P$$ and $$Q$$ are plotted on a line.

1. Find a point $$R$$ so that a 180-degree rotation with center $$R$$ sends $$P$$ to $$Q$$ and $$Q$$ to $$P$$.
2. Is there more than one point $$R$$ that works for part a?

### Problem 4

In the picture triangle $$A’B’C’$$ is an image of triangle $$ABC$$ after a rotation. The center of rotation is $$D$$.

1. What is the length of side $$B’C’$$? Explain how you know.
2. What is the measure of angle $$B$$? Explain how you know.
3. What is the measure of angle $$C$$? Explain how you know.
(From Unit 1, Lesson 7.)

### Problem 5

The point $$(\text-4,1)$$ is rotated 180 degrees counterclockwise using center $$(0,0)$$. What are the coordinates of the image?

A:

$$(\text-1,\text-4)$$

B:

$$(\text-1,4)$$

C:

$$(4,1)$$

D:

$$(4,\text-1)$$

(From Unit 1, Lesson 6.)