Question

rotate the figure 180° counterclockwise 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 are parallel in the final figure. the final angle measures are the same as the original angle measures. the final side lengths are longer than the original side lengths. the original figure and the final figure are congruent.

Explanation:

Step1: Recall rotation properties

A 180 - degree counter - clockwise rotation about the origin is a rigid transformation. Rigid transformations preserve shape and size.

Step2: Analyze parallel sides

Parallel lines remain parallel after a rotation. So, if two sides are parallel in the original figure, they are parallel in the final figure. This statement is True.

Step3: Analyze angle measures

Rigid transformations preserve angle measures. So, the final angle measures are the same as the original angle measures. This statement is True.

Step4: Analyze side lengths

Rigid transformations preserve side lengths. So, the final side lengths are equal to the original side lengths, not longer. This statement is False.

Step5: Analyze congruence

Since a 180 - degree rotation is a rigid transformation and rigid transformations preserve shape and size, the original figure and the final figure are congruent. This statement is True.

Answer:

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