,在棱长为1的正方体ABCD -A1B1C1D1中,M和N分别是AB1和BB1中点,若E、F分别是C
,在棱长为1的正方体ABCD -A1B1C1D1中,M和N分别是AB1和BB1中点,若E、F分别是C
若E、F分别为CC1、BD的中点,求证:A 1F垂直 平面BDE
若E、F分别为CC1、BD的中点,求证:A 1F垂直 平面BDE
数学人气:407 ℃时间:2019-08-21 19:33:49
优质解答
连接AFC,作FG∥BC交CD于点G,连接D1G,故AA1⊥BD,AC⊥BD,DE⊥GD1,A1D1⊥DE,故BD⊥面AA1C,DE⊥面A1GD1,又A1F在面AA1C和面A1FGD1上,故BD⊥A1F,DE⊥A1F,故A1F⊥面BDE.
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