四面体是三角形在空间的推广 ,因此三角形的许多性质可以推广到四面体上去 .本文以向量为工具 ,把三角形的余弦定理、勾股定理以及“在直角三角形中 ,30°的角所对的边是斜边的一半”等 4个定理推广到四面体上 .定理 1　 (四面体的余弦定理 )四面体C-AOB中 ,若CO垂直于平面AOB Tetrahedron is a generalization of triangles in space, so many properties of triangles can be generalized to tetrahedrons. This paper uses vector as a tool to put the cosine theorem, Pythagorean theorem of triangles and the angle of 30° in a right-angled triangle. The side is a half of the hypotenuse" and other four theorems are generalized to the tetrahedron. Theorem 1 (The cosine theorem of the tetrahedron) In the tetrahedron C-AOB, if the CO is perpendicular to the plane AOB