Question

rotate the figure 270° clockwise about the origin. then decide if each statement about rotated figures is true or false.
statement about rotated figures true false
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 larger than the original angle measures.
the original figure and the final figure may not be congruent.

Explanation:

Step1: Recall rotation properties

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

Step2: Analyze parallelism statement

Parallel lines remain parallel after rotation. So, if two sides are parallel in the original figure, they are parallel in the final figure. 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 side - length statement

Since rotation is a rigid - motion, side lengths are preserved. So, the statement "The final side lengths are the same as the original side lengths" is True.

Step4: Analyze angle - measure statement

Angle measures are preserved in a rotation. So, the statement "The final angle measures are larger than the original angle measures" is False.

Step5: Analyze congruence statement

A rotation is a rigid - motion, and rigid - motion transformations produce congruent figures. So, the statement "The original figure and the final figure may not be congruent" is False.

Answer:

If two sides are parallel in the original figure, then those sides may not be parallel in the final figure: False
The final side lengths are the same as the original side lengths: True
The final angle measures are larger than the original angle measures: False
The original figure and the final figure may not be congruent: False