Question

rotate the figure 90° counterclockwise about the origin. then decide if each statement about rotated figures is true or false. statement about rotated figures true false the final side lengths are shorter than the original side lengths. the final angle measures are smaller than the original angle measures. the original figure and the final figure are congruent. if two sides are parallel in the original figure, then those sides may not be parallel in the final figure.

Explanation:

Step1: Recall rotation properties

A 90 - degree counter - clockwise rotation about the origin is a rigid transformation. Rigid transformations preserve side lengths and angle measures.

Step2: Analyze side - length statement

Since rotation is a rigid transformation, side lengths are preserved. So, the statement "The final side lengths are shorter than the original side lengths" is false.

Step3: Analyze angle - measure statement

Angle measures are also preserved in a rigid transformation. So, the statement "The final angle measures are smaller than the original angle measures" is false.

Step4: Analyze congruence statement

Because side lengths and angle measures are preserved, the original figure and the final figure are congruent. So, the statement "The original figure and the final figure are congruent" is true.

Step5: Analyze parallel - side statement

Parallelism of lines is preserved under rotation. If two sides are parallel in the original figure, they are parallel in the final figure. 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.

Answer:

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