Dilation does not preserve congruence. True or False
The Correct Answer and Explanation is:
True. Dilation does not preserve congruence.
In geometry, dilation is a transformation that changes the size of a figure while maintaining its shape. Specifically, dilation enlarges or reduces a figure by a scale factor relative to a fixed center, but it does not preserve the size of the object. While the figure still retains its proportionality and shape, the absolute distances between points in the figure are altered by the dilation factor.
Congruence means that two figures are identical in both size and shape. When a transformation preserves congruence, it does not change the size of the figure. Common transformations that preserve congruence include translations, rotations, and reflections. These transformations can reposition or flip a figure but do not affect its size.
Dilation, on the other hand, involves changing the size of the figure. For example, if a triangle undergoes a dilation with a scale factor greater than 1, the triangle will become larger, but its angles and relative side lengths will remain the same. Similarly, if the scale factor is less than 1, the figure will shrink. In either case, the resulting figure is not congruent to the original, since their sizes are different, even though their shape is preserved.
Thus, dilation does not preserve congruence because it changes the size of the figure, even if the proportions and angles remain the same. Therefore, the statement is True.
