This paper presents a new design concept for a morphing triangle-shaped compliant mechanism. The novel design is a bistable mechanism that has one changeable side. These morphing triangles may be arrayed to create shape-morphing structures. The mechanism design was based on a six-bar dwell mechanism that can fit in a triangle shape and has stable positions at the motion-limit (dead-center) positions. An example of the triangle-shaped compliant mechanism was designed and prototyped: an isosceles triangle with a vertex that changes from 120 deg to 90 deg and vice versa. Three of these in the 120-deg configuration lie flat and when actuated to the 90-deg configuration become a cube corner. This design may be of use for folding and packaging assistance. The mechanism was designed using geometric constraint programming. Force and potential energy analyses characterize the triangle mechanism’s stability. Because of its dead-center motion limits, the vertex angle of the triangle cannot be extended past the range of 90–120 deg, in spite of the mechanism’s compliant joints. Furthermore, because it is a dwell mechanism, the vertex angle is almost immobile near its stable configurations, although other links in the mechanism move. This makes the stable positions of the vertex angle robust against stress relaxation and manufacturing errors. We believe this is the first demonstration of this kind of robustness in bistable mechanisms.