To determine the angle of rotation, you measure the angle formed by connecting corresponding vertices to the center point of rotation. In Exercise 1, measure ∠π΄π·′π΄′. What happened to ∠π·? Can you see that π· is the center of rotation, therefore, mapping π·′ onto itself? Before leaving Exercise 1, try drawing ∠π΅π·′π΅′. Do you get the same angle measure? What about ∠πΆπ·′πΆ′?

Do not include units (º) in your answer.

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Try finding the angle and direction of rotation for Exercise 2 on your own.

Do not include units (º) in your answer.

Did you draw ∠π·πΈπ·′ or ∠πΆπΈπΆ′?

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Now that you can find the angle of rotation, let’s move on to finding the center of rotation. Follow the directions below to locate the center of rotation, taking the figure at the top right to its image at the bottom left.

- Draw a segment connecting points π΄ and π΄′.
- Using a compass and straightedge, find the perpendicular bisector of this segment.
- Draw a segment connecting points π΅ and π΅′.
- Find the perpendicular bisector of this segment.
- The point of intersection of the two perpendicular bisectors is the center of rotation. Label this point π.

Justify your construction by measuring ∠π΄ππ΄′ and ∠π΅ππ΅′. Did you obtain the same measure?

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Find the center of rotation and angle of rotation for Exercise 4.

Do not include units (º) in your answer.

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Find the center of rotation and angle of rotation for Exercise 5.

Do not include units (º) in your answer.

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How does rotation π of degree π about a center πΆ affect the points of the plane?

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