Final answer:
In mathematics, both translation and reflection result in congruent pre-images and images, while dilation does not unless the scale factor is one. Rotation also results in congruent figures.
Step-by-step explanation:
In the realm of Mathematics, specifically in geometry, there are several types of transformations that can be applied to figures. One transformation where the pre-image and the image are congruent figures is known as a translation. Translation involves sliding the figure in any direction without rotating or flipping it. The figure maintains its shape and size, and thus the pre-image and the image are congruent. Another transformation is reflection, which is flipping a figure over a line, creating a mirror image, which is also congruent to the pre-image. On the other hand, dilation involves resizing the figure, which would not keep the image congruent unless the scale factor is one. Lastly, rotation involves turning the figure around a fixed point, which also results in congruent pre-image and image.