A rigid motion of Euclidean space is a transformation that preserves the distance between every pair of points, and hence is an isometry. Every rigid motion of the plane is a composition of translations, rotations, and reflections. A rigid motion maps each geometric figure to a congruent figure.
Rigid Motion
See also
Composition, Congruent Triangles, Distance, Euclidean Motion, Euclidean Space, Isometry, Plane, Reflection, Rotation, TranslationExplore with Wolfram|Alpha
References
Courant, R. and Robbins, H. What Is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. Oxford, England: Oxford University Press, p. 141, 1996.Graustein, W. C. Introduction to Higher Geometry. New York: Macmillan, pp. 84-85 and 89-91, 1930.Referenced on Wolfram|Alpha
Rigid MotionCite this as:
Weisstein, Eric W. "Rigid Motion." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RigidMotion.html