Question

properties of dilations
a dilation is a nonrigid transformation that can produce
enlarged or reduced images from a given pre - image.
how do you know that a dilation will produce similar
figures? explain.

Explanation:

Dilation scales all sides of a pre-image by a constant scale factor \( k \), so corresponding sides are proportional. Corresponding angles remain unchanged (congruent) because scaling does not alter angle measures. Two figures with proportional sides and congruent corresponding angles are similar by the definition of similar figures.

Answer:

A dilation produces similar figures because it scales all sides by a constant factor (proportional sides) and preserves corresponding angles (congruent angles), which meets the definition of similar figures.