Question

reflect the figure across the y - axis. then decide if each statement about reflected figures is true or false. statement about reflected figures: 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 longer than the original side lengths. the original figure and the final figure are congruent.

Explanation:

Step1: Recall reflection properties

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

Step2: Analyze parallelism statement

Parallel lines in the original figure remain parallel after reflection across the y - axis because reflection is a rigid transformation that does not change the orientation of lines in terms of parallelism. So, "If two sides are parallel in the original figure, then those sides are parallel in the final figure" is True.

Step3: Analyze angle - measure statement

Since reflection is a rigid transformation, it preserves angle measures. So, "The final angle measures are the same as the original angle measures" is True.

Step4: Analyze side - length statement

Reflection is a rigid transformation that preserves side lengths. So, "The final side lengths are longer than the original side lengths" is False.

Step5: Analyze congruence statement

Because reflection preserves all side lengths and angle measures, the original figure and the final figure are congruent. So, "The original figure and the final figure are congruent" is True.

Answer:

1. True
2. True
3. False
4. True