Which of these properties are not preserved by a dilation?

A dilation is a type of similarity transformation that scales a figure by a certain factor relative to a fixed point, known as the center of dilation. While dilations preserve some geometric properties, they do not preserve others. Here's a breakdown: ### **Properties Preserved by Dilation:** 1. **Shape:** The overall shape of the figure remains unchanged. 2. **Angles:** All angles within the figure remain the same. 3. **Parallelism:** Parallel lines remain parallel after dilation. ### **Properties **Not** Preserved by Dilation:** 1. **Length:** The actual lengths of line segments are scaled by the dilation factor, so they are not preserved. 2. **Area:** The area of the figure changes by the square of the dilation factor. 3. **Congruence:** Since lengths are not preserved, figures are not congruent after dilation unless the dilation factor is 1 (which means no dilation occurs). ### **Summary:** Dilation maintains the shape and angles of figures but alters their size. Therefore, **length and area are not preserved** under dilation. **Answer:** Exact lengths and sizes (such as lengths of segments and the area) are not preserved by a dilation.