A modular furniture system, in which one or more triangular frames are assembled with a leg support system in any of numerous configurations. Cushions or flat surfaces can be supported by the triangular frames to form chairs, beds, sofas, tables, and many other pieces of furniture. Triangle frames are assembled with the leg support system using frame hinges, which can include ring portions that slide over the tops of the leg support system and flanges that attach to the triangular frames.