如图所示,三棱柱ABC-A1B1C1,D是BC的中点,D1是B1C1的中点. 求证:(1)A1B∥平面AC1D; (2)平面A1BD1∥平面AC1D.

问题描述:

如图所示,三棱柱ABC-A1B1C1,D是BC的中点,D1是B1C1的中点.
求证:(1)A1B∥平面AC1D;
(2)平面A1BD1∥平面AC1D.

(1)证明:如图,连结A1C交AC1于点E,连结DE,∵四边形A1ACC1是平行四边形,∴E是A1C的中点.连结ED,∵A1B∥平面AC1D,平面A1BC∩平面AC1D=ED,∴A1B∥ED.∵A1B不包含于平面AC1D,ED⊂平面AC1D,∴A1B∥平面AC1D...