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 true false the final angle measures are smaller than the original angle measures. if two sides are parallel in the original figure, then those sides are parallel in the final figure. the final side lengths are the same as the original side lengths. the original figure and the final figure are congruent.

Explanation:

Step1: Recall rotation properties

A 90 - degree clock - wise rotation about the origin is a rigid transformation. Rigid transformations preserve angle measures, side lengths, and parallelism.

Step2: Analyze the first statement

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

Step3: Analyze the second statement

Parallelism is preserved under rotation. If two sides are parallel in the original figure, they are parallel in the rotated figure. So, this statement is true.

Step4: Analyze the third statement

Side lengths are preserved in a rigid transformation like rotation. So, the statement "The final side lengths are the same as the original side lengths" is true.

Step5: Analyze the fourth statement

Since angle measures and side lengths are preserved, the original figure and the rotated figure are congruent. So, this statement is true.

Answer:

The final angle measures are smaller than the original angle measures: False
If two sides are parallel in the original figure, then those sides are parallel in the final figure: True
The final side lengths are the same as the original side lengths: True
The original figure and the final figure are congruent: True