题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020235905-53619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020235905-81165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020235905-53619.png)
(Ⅰ)证明:OD//平面ABC;
(Ⅱ)能否在EM上找一点N,使得ON⊥平面ABDE?若能,请指出点N的位置,并加以证明;若不能,请说明理由.
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020235905-84827.png)
答案
解析
∴OF∥EA且OF=
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020235906-69140.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020235906-69140.png)
∴OF∥DB,OF=DB,
∴四边形BDOF是平行四边形。
∴OD∥FB
第二问中,当N是EM中点时,ON⊥平面ABDE。 ………7分
证明:取EM中点N,连结ON、CM, AC=BC,M为AB中点,∴CM⊥AB,
又∵面ABDE⊥面ABC,面ABDE
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020235906-94944.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020235906-84768.png)
∴CM⊥面ABDE,∵N是EM中点,O为CE中点,∴ON∥CM,
∴ON⊥平面ABDE。
核心考点
试题【如图,平面ABDE⊥平面ABC,ACBC,AC=BC=4,四边形ABDE是直角梯形,BDAE,BDBA,AE=2BD=4,O、M分别为CE、AB的中点.(Ⅰ)证】;主要考察你对空间几何体的结构特征等知识点的理解。[详细]
举一反三
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![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020235856-23045.png)
(Ⅰ)求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020235857-19288.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020235857-22503.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020235857-55712.png)
(Ⅱ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020235857-68405.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020235856-30383.png)
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![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020235842-93786.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020235843-63502.png)
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A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020235829-41920.png)
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![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020235830-18397.jpg)
(1)求三棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020235830-49076.png)
(2)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020235831-87512.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020235831-37809.png)
(3)若棱
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020235831-38677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020235831-92468.png)
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![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020235816-20762.png)
(I)判别MN与平面AEF的位置关系,并给出证明;
(II)求多面体E-AFMN的体积.
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020235816-27181.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020235816-57579.png)
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