a triangle is a polygon with three edges and three vertices. it is one of the basic shapes in geometry...in euclidean geometry any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane (i.e. a two-dimensional euclidean space). in other words, there is only one plane that contains that triangle, and every triangle is contained in some plane. if the entire geometry is only the euclidean plane, there is only one plane and all triangles are contained in it; however, in higher-dimensional euclidean spaces, this is no longer true.