Grade 8 | Unit 1 | Lesson 9: Moves in Parallel | Practice Problems

Draw parallel lines \(AB\) and \(CD\). Pick any point \(E\). Rotate \(AB\) 90 degrees clockwise around \(E\). Rotate line \(CD\) 90 degrees clockwise around \(E\). What do you notice?

Evaluate responses using AI:

OFF

Use the diagram to find the measures of each angle. Explain your reasoning. \(m{\angle ABC}\)

Evaluate responses using AI:

OFF

Use the diagram to find the measures of each angle. Explain your reasoning. \(m{\angle EBD}\)

Evaluate responses using AI:

OFF

Use the diagram to find the measures of each angle. Explain your reasoning. \(m{\angle ABE}\)

Evaluate responses using AI:

OFF

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 \(P\).

Evaluate responses using AI:

OFF

Points \(P\) and \(Q\) are plotted on a line. Is there more than one point \(R\) that works for part a?

Evaluate responses using AI:

OFF

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 \(B’C’\)? Explain how you know.

Evaluate responses using AI:

OFF

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 measure of angle \(B\)? Explain how you know.

Evaluate responses using AI:

OFF

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 measure of angle \(C\)? Explain how you know.

Evaluate responses using AI:

OFF

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

• \((\text-1,\text-4)\)

• \((\text-1,4)\)

• \((4,1)\)

• \((4,\text-1)\)