本文意在将平面几何里的勾股定理推广到三维空间(如下图),并给出三种不同的证法。命题:设三棱锥O-ABC的三条侧棱OA,OB,OC两两垂直,则有:S2△ABC=S2△OAB+S2△OBC+S2△OAC This article intends to extend the Pythagorean theorem in plane geometry to three-dimensional space (see below) and gives three different proofs. Proposition: Set the triangular pyramid O-ABC three side edges OA, OB, OC two two vertical, then: S2 △ ABC = S2 △ OAB + S2 △ OBC + S2 △ OAC