Definition
Similar figures
Similar figures have matching angles and corresponding side lengths in one constant ratio.
What it means
Imagine enlarging a shape on a copier without stretching it sideways. Every length changes by the same scale factor, while every angle stays the same. The copy may also be turned, slid, or flipped and still be similar.
Remember it
Same shape, one scale dial for every length.
Example
A triangle with side lengths 3, 4, 5 and a triangle with side lengths 6, 8, 10 are similar. Each second length is twice the matching first length, so the scale factor is 2.
Watch for
Matching only some lengths or angles is not enough; every corresponding length must use the same scale factor and every corresponding angle must match.
Common mix-up
Congruent figures have scale factor 1 and the same size; similar figures may have different sizes.
Exact meaning
Two plane figures are similar when one can be mapped to the other by a dilation followed by rigid transformations. Equivalently, corresponding angles are equal and corresponding lengths are proportional.