IM 8.1.9 Practice: Moves in Parallel

Draw parallel lines AB and CD. Pick any point E. Rotate AB 90 degrees clockwise around E. Rotate CD 90 degrees clockwise around E.

What do you notice?

Use the diagram to find the measure of the angle indicated. Explain your reasoning.

[math]m\angle ABC[/math] = ?

[math]m\angle EBD[/math] = ?

[math]m\angle ABE[/math] = ?

Points P and Q are plotted on a line. Move 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 [math]R[/math] that works?

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

What is the length of side [math]B'C'[/math]? Explain how you know.

What is the measure of angle [math]B[/math]? Explain how you know.

What is the measure of angle [math]C[/math]? Explain how you know.

The point [math]\left(-4,1\right)[/math] is rotated 180 degrees counterclockwise using center [math]\left(0,0\right)[/math]. What are the coordinates of the image?

[math]\left(4,-1\right)[/math] [math]\left(-1,-4\right)[/math] [math]\left(4,1\right)[/math] [math]\left(-1,4\right)[/math]

IM 8.1.9 Practice: Moves in Parallel

Draw parallel lines AB and CD. Pick any point E. Rotate AB 90 degrees clockwise around E. Rotate CD 90 degrees clockwise around E.

Use the diagram to find the measure of the angle indicated. Explain your reasoning.

Points P and Q are plotted on a line. Move point R so that a 180-degree rotation with center R sends P to Q and Q to P.

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

Information: IM 8.1.9 Practice: Moves in Parallel