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Congruent figures have the same shape and size. Similar figures have the same shape, but they may have different sizes.
See solution.
We are asked to explain how we can determine congruence and similarity. First, let's think about congruence.
Two figures are congruent if one can be mapped onto the other by a series of rotations, reflections, and translations. Two congruent figures have the same shape and size. This means that corresponding sides and corresponding angles are congruent.
| Verifying Congruence | |
|---|---|
| Using Measurements | Using Transformations |
| If corresponding sides and angles are congruent, the figures are congruent. | If one figure can be mapped onto the other using rotations, reflections, and translations, the figures are congruent. |
If two figures are similar, one can be mapped onto the other by a series of rotations, reflections, translations, and dilations. Similar figures have the same shape, but they may have different sizes. The corresponding angles are congruent and the ratios of the lengths of corresponding sides are proportional.
We also know two ways of determining similarity. We can use a series of rotations, reflections, translations, and dilations to map one figure onto the other. We could also measure the sides and angles of both figures. If the corresponding angles are congruent and the lengths of corresponding sides are proportional, then the figures are similar.
| Verifying Similarity | |
|---|---|
| Using Measurements | Using Transformations |
| If lengths of corresponding sides are proportional and corresponding angles are congruent, the figures are similar. | If one figure can be mapped onto the other using rotations, reflections, translations, and dilations, the figures are similar. |
