Abstract: In the course of structural mechanics, geometrical construction analysis of structures is an essential and fundamental topic. In general, geometrical construction analysis is conducted using three basic geometrical construction rules that originate from the hinged triangle rule. In order to improve the efficiency and ability of three basic rules, four auxiliary rules are proposed in this paper. With the cooperation of the auxiliary rules, the geometrical construction analysis processes of many complex systems become clear and simple, and some difficult problems that cannot be analyzed in the past only utilizing three basic rules can be solved now. Three examples are given to illustrate that the four auxiliary rules are easy to understand and effective to use.