Question

reflect the figure across the x - axis. then decide if each statement about reflected figures is true or false. statement about reflected figures: 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: Recall properties of reflection

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

Step2: Analyze side - length statement

Since reflection is a rigid - motion, the final side lengths are the same as the original side lengths. So, this statement is True.

Step3: Analyze angle - measure statement

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

Step4: Analyze parallel - side statement

Parallelism is preserved under rigid - motion transformations. If two sides are parallel in the original figure, they are parallel in the final figure. This statement is True.

Step5: Analyze congruence statement

Since side lengths and angle measures are preserved, the original figure and the final figure are congruent. So, the statement "The original figure and the final figure may not be congruent" is False.

Answer:

The final side lengths are the same as the original side lengths: True
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