In what situation will a dilation produce congruent figures?

Dilation is a transformation that changes the size of a figure while maintaining its shape and the proportion of its dimensions. When discussing dilations, the scale factor is key to determining the outcome of the transformation.

A scale factor of 1 means that the figure is being multiplied by 1, which does not alter any of the dimensions of the figure. As a result, the original figure and the dilated figure are identical in size and shape, making them congruent. This congruency happens because every point of the original figure remains in the same relative location to the center of dilation, resulting in no change in size.

In contrast, a scale factor greater than 1 (like 2) enlarges the figure, while a scale factor less than 1 (like 0.5) reduces it. Both of these transformations create figures that, while similar in shape, are not congruent because their sizes differ from the original. A negative scale factor reflects the figure as well as changes its size, which also results in a non-congruent figure.

Thus, the condition where dilation produces congruent figures is specifically when the scale factor equals 1.