Equidecomposable figures

Two plane figures are equidecomposable (or scissors congruent) if one can be cut into finitely many polygonal pieces that can be rearranged using only translations and rotations (no scaling or bending) to form the other.

Important properties

• Equidecomposable figures have equal area.

• Not all figures of equal area are equidecomposable (for example, a square and a circle are not equidecomposable in the plane).

• The pieces must be finite in number and must fit together exactly, covering the whole figure without overlap or gaps.