国标北师大版九年级上册第86页习题3·4第2题苏科版、人教版及华师大版九年级上册教材都介绍了如下一个重要的判定直角三角形的定理:“如果三角形一边上的中线等于这条边的一半,那么这个三角形是直角三角形.”本文先介绍这一定理的多种证法,而后再介绍这一定理在证明中的应用,供师生教学时参考.一、课本题的证明已知在△ABC中,CD是AB的中线,且CD=1/2AB. National Standard Beijing Normal University version of the ninth grade on the 86th page Exercise 3.4 The second issue Suke version, PEP and China Normal University version of the ninth grade textbook introduces the following an important decision right-angled triangle theorem: “If This triangle is a right-angled triangle. ”This article first introduces a variety of proofs of this theorem, and then introduces the application of this theorem in proof for teachers and students teaching For a proof of textbook title It is known that in ABC, CD is the midline of AB and CD = 1/2 AB.