Congruence in geometry

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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.

How to Cite This Entry:
Congruence in geometry. M.I. Voitsekhovskii (originator), Encyclopedia of Mathematics. URL:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098