Two shapes are similar if they have the same shape but can be different sizes. Their angles are all equal and their sides are proportional.
The scale factor is the ratio of corresponding side lengths. If one triangle has sides 3, 4, 5 and a similar triangle has sides 6, 8, 10 — the scale factor is 2.
For triangles, you only need two pairs of equal angles to prove similarity (AA rule) — the third angle must also match since angles sum to 180°.
Congruent shapes are always similar (scale factor = 1). Similar shapes are not always congruent.
Remember
Similar = same shape, possibly different size. Congruent = same shape AND same size. Congruence is a special case of similarity.
Real World
A map is similar to the real landscape — same shape, massively different size. The scale factor (e.g. 1:50,000) tells you how much smaller the map is.
Feeling ready?
Put this concept to work with a practice workout.