Question

rotate the figure 180° 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 180 - degree rotation about the origin is a rigid transformation. Rigid transformations preserve angle measures, side - lengths, and parallelism.

Step2: Analyze first statement

Since rigid transformations preserve angle measures, 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.

Step3: Analyze second statement

Parallelism is preserved under rigid transformations. So, if two sides are parallel in the original figure, they are parallel in the final figure. This statement is true.

Step4: Analyze third statement

Side - lengths are preserved under rigid transformations. So, the final side lengths are the same as the original side lengths. This statement is true.

Step5: Analyze fourth statement

Since angle measures and side - lengths are preserved, the original figure and the final figure are congruent. 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