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 shorter than the original side lengths.
the original figure and the final figure are congruent.

Explanation:

Step1: Properties of rotation

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

Step2: Analyze the first statement

If two sides are parallel in the original figure, since rotation is a rigid transformation that does not change the orientation of lines (in terms of parallelism), those sides are parallel in the final figure. So the first statement is True.

Step3: Analyze the second statement

Since 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

Because rotation is a rigid transformation, the final side lengths are equal to the original side lengths. So the third statement is False.

Step5: Analyze the fourth statement

Since rotation is a rigid transformation (preserves side - lengths and angle - measures), the original figure and the final figure are congruent. So the fourth statement is True.

Answer:

Statement about rotated figures	True	False
The final angle measures are the same as the original angle measures.	$\boxed{\text{True}}$
The final side lengths are shorter than the original side lengths.		$\boxed{\text{False}}$
The original figure and the final figure are congruent.	$\boxed{\text{True}}$