Lesson 8

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?

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

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

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?

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.

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

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

$(\text-1,4)$

$(4,1)$

$(4,\text-1)$