Question

rotate the figure 90° clockwise about the origin. then decide if each statement about rotated figures is true or false.

statement about rotated figures
if two sides are parallel in the original figure, then those sides may not be parallel in the final figure.
the final side lengths are the same as the original side lengths.
the final angle measures are smaller than the original angle measures.
the original figure and the final figure may not be congruent.

Explanation:

Step1: Properties of rotation

Rotation is a rigid transformation. Rigid transformations preserve side - lengths, angle - measures, and parallelism.

Step2: Analyze the first statement

If two sides are parallel in the original figure, after a \(90^{\circ}\) clockwise rotation about the origin (a rigid transformation), those sides will still be parallel. So the statement “If two sides are parallel in the original figure, then those sides may not be parallel in the final figure” is False.

Step3: Analyze the second statement

Since rotation is a rigid transformation, the final side lengths are the same as the original side lengths. So the statement “The final side lengths are the same as the original side lengths” is True.

Step4: Analyze the third statement

Because rotation is a rigid transformation, the final angle measures are equal to the original angle measures. So the statement “The final angle measures are smaller than the original angle measures” is False.

Step5: Analyze the fourth statement

Since rotation is a rigid transformation, the original figure and the final figure are congruent. So the statement “The original figure and the final figure may not be congruent” is False.

Answer:

1. False
2. True
3. False
4. False