We want to identify which transformations can be used to show that two figures are congruent. Congruent figures have the same shape and size.
Let's review the transformations we know.
Translation
A translation slides a figure around without turning it. It does not affect the shape or size of the figure.
Reflection
A reflection creates a mirror image of a figure. It does not affect the shape or size of the figure.
Rotation
A rotation turns a figure around a fixed point. It does not affect the shape or size of the figure.
Dilation
A dilation is an enlargement or reduction of the original figure. It does not affect the shape of a figure, but it does change the size of the figure.
A dilation changes the size of a figure. Since the preimage may not be congruent to the image, we cannot use a dilation to show that two figures are congruent.
Translations, reflections, and rotations do not change the shape or size of a figure, so they can be used to show that two figures are congruent. No matter what combination of translations, reflections, and rotations we use, the preimage and the image will have the same shape and size.
