Definition:Congruence (Geometry)

Topology
Two sets $$A, B \subset X \ $$ of a space $$X \ $$ are said to be congruent if there is an isometry $$f: X \to X \ $$ such that $$f \left({A}\right) = B \ $$.

Such an isometry is called a congruence.

Geometry
In the field of Euclidean geometry, two geometric figures are congruent if they are, informally speaking, both "the same size and shape". That is, one shape can be overlayed on the other with a series of rotations, translations, and reflections.

Specifically, all corresponding angles of the congruent shapes must have the same measurement, and all corresponding sides of the congruent shapes must be be the same length.