Definition of "congruence"

The quality of agreeing or corresponding; being suitable and appropriate.  examples

(mathematics, number theory) A relation between two numbers indicating they give the same remainder when divided by some given number.  examples

(mathematics, geometry) The quality of being isometric — roughly, the same measure and shape.  examples

(mathematics, linear algebra) Matrix similarity by an orthogonal matrix.  examples

(algebra, more generally) Any equivalence relation defined on an algebraic structure which is preserved by operations defined by the structure.  examples