Roughly, a periodic billiard path is a polygon P is called stable if any polygon P', which is sufficiently similar to P, has a periodic billiard path which bounces off the same sequence of edges. We will discuss the resolution of a conjecture of Vorobets, Galperin, and Stepin. No right triangle has a stable periodic billiard path. We will also discuss a slight generalization. Namely, stable perioidic billiards paths in acute and obtuse triangle can be distinguished by the sequence of edges they hit.