Question

reflect the figure across the x-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 may not be parallel in the final figure. the final side lengths are the same as the original side lengths. the final angle measures are smaller than the original angle measures. the original figure and the final figure may not be congruent. true false

Explanation:

For the first statement: "If two sides are parallel in the original figure, then those sides may not be parallel in the final figure."

Reflection is a rigid transformation that preserves the shape and size of the figure, including the parallelism of sides. So if sides are parallel in the original, they remain parallel in the reflected figure. Thus, the statement is false.

For the second statement: "The final side lengths are the same as the original side lengths."

Reflection is a rigid transformation, which means it does not change the length of sides. So final side lengths equal original side lengths. The statement is true.

For the third statement: "The final angle measures are smaller than the original angle measures."

Rigid transformations (like reflection) preserve angle measures. So angle measures in the final figure are equal to the original, not smaller. The statement is false.

For the fourth statement: "The original figure and the final figure may not be congruent."

Answer:

• "If two sides are parallel in the original figure, then those sides may not be parallel in the final figure.": False
• "The final side lengths are the same as the original side lengths.": True
• "The final angle measures are smaller than the original angle measures.": False
• "The original figure and the final figure may not be congruent.": False