Definition:Congruence


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


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


 * Abstract Algebra:
 * Congruence Modulo an Ideal: A concept in ideal theory.
 * Congruent Matrices
 * Congruence Relation: An equivalence on an algebraic structure which is compatible with its operation.


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