已知E,F,G,H分别是正方体ABCD-A'B'C'D的棱BC,CC',C'D'和AA'的中点已知E,F,G,H分别是正方体ABCD-A'B'C'D的棱BC,CC',C'D'和AA'的中点,O为AC与BD的交点.求证:(1)EG//平面BB'D'D;(2)平面BDF//平面B'D'H;(3)A'O⊥平面BDF.
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![已知E,F,G,H分别是正方体ABCD-A'B'C'D的棱BC,CC',C'D'和AA'的中点已知E,F,G,H分别是正方体ABCD-A'B'C'D的棱BC,CC',C'D'和AA'的中点,O为AC与BD的交点.求证:(1)EG//平面BB'D'D;(2)平面BDF//平面B'D'H;(3)A'O⊥平面BDF.](/uploads/image/z/7788367-55-7.jpg?t=%E5%B7%B2%E7%9F%A5E%2CF%2CG%2CH%E5%88%86%E5%88%AB%E6%98%AF%E6%AD%A3%E6%96%B9%E4%BD%93ABCD-A%27B%27C%27D%E7%9A%84%E6%A3%B1BC%2CCC%27%2CC%27D%27%E5%92%8CAA%27%E7%9A%84%E4%B8%AD%E7%82%B9%E5%B7%B2%E7%9F%A5E%2CF%2CG%2CH%E5%88%86%E5%88%AB%E6%98%AF%E6%AD%A3%E6%96%B9%E4%BD%93ABCD-A%27B%27C%27D%E7%9A%84%E6%A3%B1BC%2CCC%27%2CC%27D%27%E5%92%8CAA%27%E7%9A%84%E4%B8%AD%E7%82%B9%2CO%E4%B8%BAAC%E4%B8%8EBD%E7%9A%84%E4%BA%A4%E7%82%B9.%E6%B1%82%E8%AF%81%3A%281%29EG%2F%2F%E5%B9%B3%E9%9D%A2BB%27D%27D%3B%282%29%E5%B9%B3%E9%9D%A2BDF%2F%2F%E5%B9%B3%E9%9D%A2B%27D%27H%3B%283%29A%27O%E2%8A%A5%E5%B9%B3%E9%9D%A2BDF.)
已知E,F,G,H分别是正方体ABCD-A'B'C'D的棱BC,CC',C'D'和AA'的中点已知E,F,G,H分别是正方体ABCD-A'B'C'D的棱BC,CC',C'D'和AA'的中点,O为AC与BD的交点.求证:(1)EG//平面BB'D'D;(2)平面BDF//平面B'D'H;(3)A'O⊥平面BDF.
已知E,F,G,H分别是正方体ABCD-A'B'C'D的棱BC,CC',C'D'和AA'的中点
已知E,F,G,H分别是正方体ABCD-A'B'C'D的棱BC,CC',C'D'和AA'的中点,O为AC与BD的交点.求证:
(1)EG//平面BB'D'D;
(2)平面BDF//平面B'D'H;
(3)A'O⊥平面BDF.
已知E,F,G,H分别是正方体ABCD-A'B'C'D的棱BC,CC',C'D'和AA'的中点已知E,F,G,H分别是正方体ABCD-A'B'C'D的棱BC,CC',C'D'和AA'的中点,O为AC与BD的交点.求证:(1)EG//平面BB'D'D;(2)平面BDF//平面B'D'H;(3)A'O⊥平面BDF.
(1)作B′C′中点M 连接ME ∴ME‖BB′,MG‖B′D′
∴平面MEG‖平面BDD′D ∵EG∈平面MEG ∴ EG‖平面BB'D'D
(2)作DD′中点N 连接NC′ ∵BD‖B′D′ HN‖B′C′且HN=B′C
∴HB′‖NC′ ∵NC′‖DF ∴ DF‖HB′
又∵HB′∩B′D′=B′,BD∩DF=D
∴平面BDF//平面B'D'H;
(3)连接OF,A′F.设边长为2a
∴OF=√3a,A′O=√6a,A′F=3a.
∴OF²+A′O²=A′F² ∴A′O⊥OF
又∵OF∈平面BDF.∴A'O⊥平面BDF.
这类题目其实很简单的 要仔细分析 不要慌 很基础的