已知斜三棱柱ABC-A1B1C1的底面ABC是正三角形,且角A1AB=角A1AC,证明:AA1垂BC

问题描述:

已知斜三棱柱ABC-A1B1C1的底面ABC是正三角形,且角A1AB=角A1AC,证明:AA1垂BC

连结A1B、A1C.在三角形A1BA和A1CA中,AA1=AA1、AB=AC、角A1AB=角A1AC.所以,三角形A1BA全等三角形A1CA,即A1B=A1C.取BC的中点D,连结A1D、AD.因为A1B=A1C、AB=AC,所以,A1D垂直BC、AD垂BC.又A1D交AD=D,所以BC垂直平面AA1D...