Editing Wallace–Bolyai–Gerwien theorem (section)

== Formulation ==
There are several ways in which this theorem may be formulated. The most common version uses the concept of "equidecomposability" of polygons: two polygons are equidecomposable if they can be split into [[finite set|finitely many]] [[triangle]]s that only differ by some [[isometry]] (in fact only by a combination of a translation and a rotation). In this case the Wallace–Bolyai–Gerwien theorem states that two polygons are equidecomposable if and only if they have the same area.

Another formulation is in terms of [[scissors congruence]]: two polygons are scissors-congruent if they can be decomposed into finitely many polygons that are pairwise [[congruence (geometry)|congruent]]. Scissors-congruence is an [[equivalence relation]]. In this case the Wallace–Bolyai–Gerwien theorem states that the [[equivalence classes]] of this relation contain precisely those polygons that have the same area.