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 $$z \in \R, z \ne 0$$) iff $$x \,\bmod\, z = y \,\bmod\, z$$


 * Congruence Modulo m: Similar to Congruence (Number Theory) except limited to integers.


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