The Compendium Geometry is an eBook providing facts, formulas and explanations about geometry.

Congruence Transformation

Mathematically speaking, a congruence transformation is a bijective map f() between two metric spaces that preserves the distances, i.e.,

d(f(x), f(y)) = d(x,y)

where d(a,b) is the distance function. In clear text words, this means that a congruent transformation is a transformation which does not change the distance between any two points of the object being transformed.

Congruence transformations are also called isometries. Two figures that can be transformed into each other by a congruence transformation are said to be congruent. Congruence transformations of the plane include translation, rotation, reflection, glides, and the identity map. Every congruent transformation in the plane can be achieved by a maximum of three reflections.

Last Update: 2010-12-06