When Are Two Figures Congruent?

Abstract

SummaryThe title question has at least two natural answers, one global and one local. Global: “when they can be made to coincide by a rigid motion of the whole plane”; local: “when there is a one-to-one distance preserving mapping of one onto the other.” Self-evidently global implies local. We show that in fact these different notions lead to precisely the same notion of congruence.