Congruence (geometry)

Two sets in Rⁿ (and especially two shapes in R²) are called congruent if one can be mapped onto the other by a combination of a translation, rotation and reflection.

Two sets that are not congruent are called non-congruent.

 For instance:

  *                *                   *
  *                *         *        * *
  *****        *****         ***      ***
  *                *         *
  *                *

The first two figures are congruent to each other. The third is a different size, and so is similar but not congruent to the others; the fourth is different altogether. Note that congruences alter some properties, such as location and orientation, but leave others unchanged, like distances and angles. The latter sort of properties are called invariants and studying them is the essence of geometry.