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The question you provided asks:

**When you reduce or enlarge a figure, are the preimage and image congruent? Why or why not? What about their side lengths and angle measures?**

### Answer:
The **preimage** and the **image** in this case are **not congruent** if the figure is reduced or enlarged. Congruent figures must have exactly the same size and shape, which means corresponding side lengths must be identical. When a figure is reduced or enlarged, the size changes, but the shape remains the same. Therefore, the figures are **similar** but not congruent.

- **Side lengths**: In a dilation (reduction or enlargement), the side lengths of the image are proportional to the side lengths of the preimage, meaning that they increase or decrease by the same scale factor.
- **Angle measures**: The angle measures remain unchanged during dilation. Corresponding angles in similar figures are equal, so the image and preimage have the same angles.

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### Related Questions:
1. What is the difference between congruent and similar figures?
2. How do you calculate the scale factor of a dilation?
3. What are the properties of figures that undergo dilation?
4. Can two figures be congruent but not similar? Why or why not?
5. What role does dilation play in transformations in geometry?

**Tip**: Always check both side lengths and angles when determining if figures are congruent or merely similar.

When you reduce or enlarge a figure, are the preimage and image congruent? Why or why not? What about their side lengths and angle measures?

Explore how dilation affects figures in geometry, and understand why reduced or enlarged figures are not congruent but similar. Learn about proportional side lengths and unchanged angle measures, suitable for Grades 7-10 students.

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