Editing Wallace–Bolyai–Gerwien theorem (section)

== Proof sketch ==
The theorem can be understood in a few steps. Firstly, every polygon can be cut into triangles. There are a few methods for this. For [[convex polygon]]s one can cut off each [[vertex (geometry)|vertex]] in turn, while for [[concave polygon]]s this requires more care. A general approach that works for non-simple polygons as well would be to choose a [[line (geometry)|line]] not parallel to any of the sides of the polygon and draw a line parallel to this one through each of the vertices of the polygon. This will divide the polygon into triangles and [[trapezoids]], which in turn can be converted into triangles.

Secondly, each of these triangles can be transformed into a right triangle and subsequently into a [[rectangle]] with one side of length 1. Alternatively, a triangle can be transformed into one such rectangle by first turning it into a [[parallelogram]] and then turning this into such a rectangle. By doing this for each triangle, the polygon can be decomposed into a rectangle with unit width and height equal to its area.

Since this can be done for any two polygons, a "common subdivision" of the rectangle in between proves the theorem. That is, cutting the common rectangle (of size 1 by its area) according to both polygons will be an intermediate between both polygons.