| @MattJ: Yes, you can always draw a plane through the three vertices of a triangle. However, a triangle is a two-dimensional shape that can be defined on any surface. For example, you can define a triangle on the surface of the Earth with one vertex at the north pole and two on the equator, 90° longitude apart. There is a plane through the vertices but that's not the surface on which the triangle exists. (It is, by the way, an equilateral triangle with three 90° angles. Well, it is if you assume the Earth is a sphere.) |