The points and are coplanar (lie in the same plane) because of the assumed concurrency of and . Therefore, the lines and belong to the same plane and must intersect. Further, if the two triangles lie on different planes, then the point belongs to both planes. By a symmetric argument, the points and also exist and belong to the planes of both triangles. Since these two planes intersect in more than one point, their intersection is a line that contains all three points.