平行六面体ABCD-A1B1C1D1中,O1,O是底面A1B1C1D1对角线交点和ABCD对角线交点 求证：A1O//平

您好!分析：证明线面平行有两种思路：（人教版必2）      一、根据的线面平行判定定理,证明线与面内的另一条线平行；      二、根据面面平行的性质,证明直线所在的某平面与已知平面平行.证法一：如图,连接CO'.        ∵由正方体的性质有AA'//CC',且AA'=CC'               ∴四边形AA'C'C是平行四边形        ∴A'C'//AC,A'C'=AC            又∵A'O'=1/2A'C',OC=1/2AC               ∴A'O'//OC,A'O'=OC               ∴四边形A'OCO'是平行四边形        ∴A'O//CO'            又∵CO'在平面B'D'C内        ∴A'O//平面B'D'C证法二：如图,连接BA',DA'.        ∵由正方体的性质有A'D'//BC,且A'D'=BC               ∴四边形A'BCD'是平行四边形        ∴A'B//D'C           又∵CD'在平面B'D'C内        ∴A'B//平面B'D'C               同理可证A'D//平面B'D'C           又∵A'B∩A'D=A'且A'B、A'D都在平面BDA'内        ∴平面BDA'//平面B'D'C               ∵A'O在平面BDA'内        ∴A'O//平面B'D'C