Question

statement about translated figures
the final side lengths are longer than the original side lengths.
the final angle measures are larger than the original angle measures.
the original figure and the final figure are congruent.
if two sides are parallel in the original figure, then those sides may not be parallel in the final figure.

Explanation:

Step1: Recall translation properties

Translation is a rigid - motion transformation. It only moves a figure without changing its shape or size.

Step2: Analyze side - length statement

Since translation is a rigid motion, side lengths remain the same. So, the statement "The final side lengths are longer than the original side lengths" is False.

Step3: Analyze angle - measure statement

Rigid motions also preserve angle measures. So, the statement "The final angle measures are larger than the original angle measures" is False.

Step4: Analyze congruence statement

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

Step5: Analyze parallel - side statement

Parallelism of sides is also preserved under translation. So, 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:

The final side lengths are longer than the original side lengths: False
The final angle measures are larger than the original angle measures: False
The original figure and the final figure are congruent: True
If two sides are parallel in the original figure, then those sides may not be parallel in the final figure: False