如图,在正方体ABCD–A1B1C1D1中,求证:平面ACA1C1垂直平面A1BD

问题描述:

如图,在正方体ABCD–A1B1C1D1中,求证:平面ACA1C1垂直平面A1BD

ac垂直bd 设ac、bd交于O点.平面ACA1C1与A1BD的交线为A1O
A1D=A1B=BD DO=BO 所以A1O垂直BD
所以平面ACA1C1垂直平面A1BD