Wallace–Bolyai–Gerwien theorem
![By the Wallace–Bolyai–Gerwien theorem, a square can be cut into parts and rearranged into a triangle of equal area.](/Images/godic/202501/11/Triangledissection.svg5047.png")
In geometry, the Wallace–Bolyai–Gerwien theorem, named after William Wallace, Farkas Bolyai and Paul Gerwien, is a theorem related to dissections of polygons. It answers the question when one polygon can be formed from another by cutting it into a finite number of pieces and recomposing these by translations and rotations. The Wallace-Bolyai-Gerwien theorem states that this can be done if and only if two polygons have the same area.