Congruence in geometry

An equivalence relation on a set of geometrical figures (segments, angles, etc.). It is introduced either axiomatically (see Hilbert system of axioms) or on the basis of some group of transformations, most frequently of motions (cf. Motion). Thus, in Euclidean geometry (and more generally in the geometry of spaces of constant curvature), two figures are said to be congruent, or equal, if one can be taken to the other by a motion.