(1)求证:B1D1⊥AE;
(2)求证:AC∥平面B1DE.
(1)求证:B1D1⊥AE;
(2)求证:AC∥平面B1DE.
∵ABCD是正方形,∴AC⊥BD.∵CE⊥面ABCD,
∴CE⊥BD.又AC∩CE=C,∴BD⊥面ACE.
∵AE
面ACE,∴BD⊥AE.
∴B1D1⊥AE.
(2)取BB1的中点F,连结AF、CF、EF.
∵E、F是CC1、BB1的中点,∴CE
B1F.
∴四边形B1FCE是平行四边形.∴CF∥B1E.
∵E,F是CC1、BB1的中点,∴EF
BBC.又BC
AD,∴EF
AD.
∴四边形ADEF是平行四边形.∴AF∥ED.
∵AF∩CF=F,B1E∩ED=E,∴平面ACF∥面B1DE.
又AC
平面ACF,∴AC∥面B1DE.