Lesson 8: Practice Problems

Problem 1

- Draw parallel lines $A B$ and $C D$ .
- Pick any point $E$ . Rotate $A B$ 90 degrees clockwise around $E$ .
- Rotate $C D$ 90 degrees clockwise around $E$ .
What do you notice?

Problem 2

Use the diagram to find the measure of each angle.

Line EC is intersected at point B by line AD. Angle CBD is 45 degrees.

$m ∠ A B C$
$m ∠ E B D$
$m ∠ A B E$

Problem 3

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

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

Problem 4 From Unit 1 Lesson 6

In the picture triangle $A^{'} B^{'} C^{'}$ is an image of triangle $A B C$ after a rotation. The center of rotation is $D$ .

Triangle A prime, B prime, C prime is an image of triangle A, B, C after rotation around another point, D. Side B, C has length 4. Angle B prime has measure 52 degrees. Angle C prime has measure 50 degrees.

What is the length of side $B^{'} C^{'}$ ? Explain how you know.
What is the measure of angle $B$ ? Explain how you know.
What is the measure of angle $C$ ? Explain how you know.

Problem 5 From Unit 1 Lesson 5

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

$(- 1, - 4)$
$(- 1, 4)$
$(4, 1)$
$(4, - 1)$