Let F_0 and F_1 denote two directly similar figures in the plane, where P_1 element F_1 corresponds to P_0 element F_0 under the given similarity. Let r element (0, 1), and define F_r = {(1 - r) P_0 + r P_1 :P_0 element F_0, P_1 element F_1}. Then F_r is also directly similar to F_0.

directly similar | Finsler-Hadwiger theorem