convex polygon decomposed into 2 similar to the first polygons
Source: Spanish Mathematical Olympiad 1969 P5
December 4, 2022
geometryconvex polygonsimilaritycombinatorial geometrytiles
Problem Statement
Show that a convex polygon with more than four sides cannot be decomposed into two others, both similar to the first (directly or inversely), by means of a single rectilinear cut. Reasonably specify which are the quadrilaterals and triangles that admit a decomposition of this type.