Definition:Congruence


 * Congruence (Geometry): Two geometric figures are congruent if they are both "the same size and shape".


 * Congruence (Metric Spaces): Two subsets of a space are congruent if there is an isometry between them.


 * Congruence Modulo an Ideal: A concept in ideal theory.


 * Congruence (Number Theory): Two real numbers $x$ and $y$ are congruent (modulo $z \in \R$) iff $x \bmod z = y \bmod z$


 * Congruence Relation: An equivalence on an algebraic structure which is compatible with its operation.