We are asked to explain how we can show that two figures are either congruent or similar to one another. Let's first consider congruent figures.

Congruent Figures

Recall what it means for two figures to be congruent.

Congruent Figures
Two figures are congruent when they have the same shape and size.

When two figures are congruent, one can be mapped onto the other using a sequence of translations, rotations, and reflections. This is because none of these transformations affects the shape or size of a figure.

Then, to show that two figures are congruent, we can find a sequence of translations, rotations, and reflections that maps one figure onto the other.

Similar Figures

Recall what it means when two figures are similar.

Similar Figures
Two figures are similar when they have the same shape, but they may have different sizes.

When two figures are similar, one can be mapped onto the other using a sequence of translations, rotations, reflections, and dilations. This is because none of these transformations affects the shape of a figure.

To show that two figures are similar, we can find a sequence of translations, rotations, and reflections that maps one figure onto the other.

Exercise