Homothety and constructing similar polygons

To construct a similar polygon, pick any point O in the plane and draw rays from O through every vertex of the given polygon. On each ray mark OA₁ = k·OA, OB₁ = k·OB, and so on (with k < 1 the polygon is reduced). Joining the new vertices in order gives the similar polygon. Justification: triangles OAD and OA₁D₁ are similar, so corresponding sides are in ratio k; corresponding angles are equal as well. The point O may lie outside the polygon, inside it, at a vertex or on a side; the resulting polygons are all congruent. The construction is done with a compass and ruler or on squared paper.