Equidissection Equidissection In geometry, an equidissection is a partition of a polygon into triangles of equal area. The study of equidissections began in the late 1960s with Monsky's theorem, which states that a square cannot be equidissected into an odd number of triangles. In fact, most polygons cannot be equidissected at all. Much of the literature is aimed at generalizing Monsky's theorem to broader classes of polygons. The general question is: Which polygons can be equidissected into how many pieces? Particular attention has been given to trapezoids, kites, regular polygons, centrally symmetric polygons, polyominos, and hypercubes. Equidissections do not have many
Similarity (geometry) are in proportion, and corresponding angles of similar polygons have the same measure. This article assumes that a scaling can have a scale factor of 1, so that all congruent shapes are also similar, but some school textbooks specifically exclude congruent triangles from their definition of similar triangles by insisting that the sizes must be different if the triangles are to qualify as similar. In geometry two triangles, and , are similar if and only if corresponding angles have the same measure: this implies that they are similar if and only if the lengths of corresponding sides are proportional. It