Question

statement about rotated 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 shorter than the original side lengths.
the original figure and the final figure are congruent.

Explanation:

To determine the correctness of each statement about rotated figures, we analyze the properties of rotation (a type of rigid transformation):

1. "If two sides are parallel in the original figure, then those sides are parallel in the final figure."

Rotation preserves the shape and orientation relationships. Parallel lines remain parallel after rotation. So this is True.

1. "The final angle measures are the same as the original angle measures."

Rigid transformations (like rotation) preserve angle measures. So this is True.

1. "The final side lengths are shorter than the original side lengths."

Rotation is a rigid transformation, so side lengths are preserved (not shortened). So this is False.

1. "The original figure and the final figure are congruent."

Rigid transformations (rotation) produce congruent figures (same shape and size). So this is True.

Final Answers (Matching Each Statement):

1. If two sides are parallel in the original figure, then those sides are parallel in the final figure: $\boldsymbol{\text{True}}$
2. The final angle measures are the same as the original angle measures: $\boldsymbol{\text{True}}$
3. The final side lengths are shorter than the original side lengths: $\boldsymbol{\text{False}}$
4. The original figure and the final figure are congruent: $\boldsymbol{\text{True}}$

Answer:

To determine the correctness of each statement about rotated figures, we analyze the properties of rotation (a type of rigid transformation):

1. "If two sides are parallel in the original figure, then those sides are parallel in the final figure."

Rotation preserves the shape and orientation relationships. Parallel lines remain parallel after rotation. So this is True.

1. "The final angle measures are the same as the original angle measures."

Rigid transformations (like rotation) preserve angle measures. So this is True.

1. "The final side lengths are shorter than the original side lengths."

Rotation is a rigid transformation, so side lengths are preserved (not shortened). So this is False.

1. "The original figure and the final figure are congruent."

Rigid transformations (rotation) produce congruent figures (same shape and size). So this is True.

Final Answers (Matching Each Statement):

1. If two sides are parallel in the original figure, then those sides are parallel in the final figure: $\boldsymbol{\text{True}}$
2. The final angle measures are the same as the original angle measures: $\boldsymbol{\text{True}}$
3. The final side lengths are shorter than the original side lengths: $\boldsymbol{\text{False}}$
4. The original figure and the final figure are congruent: $\boldsymbol{\text{True}}$