Select all the statements that must be true for any scaled copy Q of Polygion P.

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To determine which statements must be true for any scaled copy $$ Q $$ of a polygon $$ P $$, let's consider the fundamental properties of scaling transformations in geometry.

### Properties of Scaled Copies (Similarity Transformations)

1. **Similarity**:
   - **Statement**: $$ Q $$ is similar to $$ P $$.
   - **Explanation**: Scaling is a type of similarity transformation. This means that the shape of $$ Q $$ is identical to $$ P $$, but its size is different.

2. **Congruent Corresponding Angles**:
   - **Statement**: All corresponding angles in $$ Q $$ and $$ P $$ are congruent.
   - **Explanation**: Scaling affects the size but not the angles of the polygon. Thus, each angle in $$ Q $$ matches the corresponding angle in $$ P $$ exactly.

3. **Proportional Corresponding Sides**:
   - **Statement**: The ratios of corresponding side lengths in $$ Q $$ to $$ P $$ are equal to the scaling factor.
   - **Explanation**: If the scaling factor is $$ k $$, then each side length in $$ Q $$ is $$ k $$ times the corresponding side length in $$ P $$.

4. **Perimeter Scaling**:
   - **Statement**: The perimeter of $$ Q $$ is $$ k $$ times the perimeter of $$ P $$.
   - **Explanation**: Since each side is scaled by $$ k $$, the entire perimeter scales proportionally.

5. **Area Scaling**:
   - **Statement**: The area of $$ Q $$ is $$ k^2 $$ times the area of $$ P $$.
   - **Explanation**: Area scales with the square of the scaling factor because both dimensions (length and width) are scaled.

### Summary of Must-Be-True Statements

- **Similarity**: $$ Q $$ must be similar to $$ P $$.
- **Angle Congruence**: All corresponding angles in $$ Q $$ and $$ P $$ are equal.
- **Side Proportions**: The ratio of corresponding sides is constant and equal to the scaling factor.
- **Perimeter Proportion**: The perimeter scales linearly with the scaling factor.
- **Area Proportion**: The area scales with the square of the scaling factor.

If you have specific statements or options you'd like to evaluate, feel free to provide them, and I can help determine which are necessarily true based on these principles.
For any scaled copy $$ Q $$ of polygon $$ P $$, the following must be true: 1. $$ Q $$ is similar to $$ P $$. 2. All corresponding angles in $$ Q $$ and $$ P $$ are equal. 3. The ratios of corresponding side lengths in $$ Q $$ to $$ P $$ are equal to the scaling factor. 4. The perimeter of $$ Q $$ is $$ k $$ times the perimeter of $$ P $$. 5. The area of $$ Q $$ is $$ k^2 $$ times the area of $$ P $$. These properties ensure that the shape, angles, and measurements of $$ Q $$ are consistent with the scaling transformation applied to $$ P $$.

Select all the statements that must be true for any scaled copy Q of Polygion P.

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