Question

rotate the figure 270° counterclockwise 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 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 may not be congruent. if two sides are parallel in the original figure, then those sides may not be parallel in the final figure.

Explanation:

• Angle Measures: Rotation is a rigid transformation. Rigid transformations preserve angle measures. So, the final angle measures are the same as the original angle measures. This statement is True.
• Side Lengths: Rotation is a rigid transformation. Rigid transformations preserve side - lengths. So, the final side lengths are equal to the original side lengths. The statement "The final side lengths are longer than the original side lengths" is False.
• Congruence: Rotation is a rigid transformation. Rigid transformations produce congruent figures. So, the original figure and the final figure are congruent. The statement "The original figure and the final figure may not be congruent" is False.
• Parallel Sides: Rotation is a rigid transformation. Rigid transformations preserve parallelism. If two sides are parallel in the original figure, then those sides are parallel in the final figure. The statement "If two sides are parallel in the original figure, then those sides may not be parallel in the final figure" is False.

Answer:

Statement about rotated figures	True	False
The final side lengths are longer than the original side lengths.		$\square$
The original figure and the final figure may not be congruent.		$\square$
If two sides are parallel in the original figure, then those sides may not be parallel in the final figure.		$\square$