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 the same as the original side lengths. the final angle measures are the same as the original angle measures. if two sides are parallel in the original figure, then those sides are parallel in the final figure. the original figure and the final figure may not be congruent.

Explanation:

Step1: Property of rotation

Rotation is a rigid transformation. Rigid transformations preserve side - lengths and angle - measures.

Step2: Analyze the first statement

Since rotation is a rigid transformation, the final side lengths are the same as the original side lengths. So the first statement is True.

Step3: Analyze the second statement

As rotation is a rigid transformation, the final angle measures are the same as the original angle measures. So the second statement is True.

Step4: Analyze the third statement

Rigid transformations also preserve parallelism. If two sides are parallel in the original figure, they are parallel in the rotated figure. So the third statement is True.

Step5: Analyze the fourth statement

Since rotation is a rigid transformation, the original figure and the rotated (final) figure are congruent. So the fourth statement is False.

Answer:

Statement about rotated figures	True	False
The final angle measures are the same as the original angle measures.	True
If two sides are parallel in the original figure, then those sides are parallel in the final figure.	True
The original figure and the final figure may not be congruent.		False