Abstract: The geometric composition analysis of plane system is one of the key contents of structural mechanics. However, the conventional three basic composition rules are still very difficult in the geometric composition analysis of complex plane system. Therefore, based on the equivalence idea, three equivalent analysis ideas for the geometric composition analysis of complex plane systems are proposed: virtual-real hinge equivalence, rigid-plate equivalence replacement and constrained translation equivalence. Combining with the three basic composition rules and comprehensively using of the three equivalent ideas, the feasibility and efficiency of the three equivalent ideas are effectively verified through case analysis of typical complex plane system. The three equivalent ideas provide new ideas and ways for the geometric composition analysis of complex plane system.