Question

rotate the figure 180° clockwise about the origin. then decide if each statement about rotated figures is true or 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: Properties of rotation

Rotation is a rigid transformation. Rigid transformations preserve side - lengths and angle - measures.
For the first statement: Since rotation is a rigid transformation, the final side lengths are the same as the original side lengths. So, the statement "The final side lengths are the same as the original side lengths" is True.
For the second statement: Because rotation is a rigid transformation, the final angle measures are the same as the original angle measures. So, the statement "The final angle measures are the same as the original angle measures" is True.
For the third statement: Rotation preserves the shape and orientation relationships (such as parallelism). If two sides are parallel in the original figure, then those sides are parallel in the final figure. So, the statement "If two sides are parallel in the original figure, then those sides are parallel in the final figure" is True.
For the fourth statement: Rotation is a rigid transformation. Rigid transformations produce congruent figures. So, the statement "The original figure and the final figure may not be congruent" is False.

Answer:

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