题目
题型:不详难度:来源:
(1)求证:平面A B1D1∥平面EFG;
(2)求证:平面AA1C⊥面EFG .
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021023055-16259.gif)
答案
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021023056-26217.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021023056-20884.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021023056-26217.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021023056-20884.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021023056-26217.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021023056-76828.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021023056-77994.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021023056-30897.gif)
∵E,F分别为BC,CD的中点
∴EF∥BD ∴EF∥
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021023056-77994.gif)
∵EF
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021023057-65589.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021023056-77994.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021023057-93222.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021023056-77994.gif)
同理
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021023057-13569.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021023056-77994.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021023057-64361.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021023057-13569.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021023057-29296.gif)
∴平面A B1D1∥平面EFG ……………5分
(2)在正方体ABCD-A1B1C1D1 ∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021023058-31913.gif)
∵EF
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021023057-65589.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021023058-31913.gif)
∵ABCD为正方形 ∴AC
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021023058-71564.gif)
∵EF∥BD ∴AC
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021023058-71564.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021023058-21219.gif)
∴EF
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021023058-71564.gif)
∵EF
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021023057-65589.gif)
核心考点
试题【(本小题满分10分)如图,在棱长为ɑ的正方体ABCD-A1B1C1D1中,E、F、G分别是CB、CD、CC1的中点.(1)求证:平面A B1D1∥平面EFG;(】;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
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022824-55220.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022824-12064.gif)
A.若![]() ![]() ![]() | B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() | D.若![]() ![]() ![]() |
如图,在四棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022714-20824.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022714-82413.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022714-73670.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022715-52062.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022715-36020.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022715-97838.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022715-45619.gif)
(Ⅰ)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022716-36285.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022716-88705.gif)
(Ⅱ)侧棱
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022716-81967.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022716-52769.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022716-86455.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022716-88705.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022717-74969.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022700-67109.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022700-35172.png)
A.若![]() ![]() ![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022642-15960.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022642-81249.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022642-47233.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022643-90564.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022643-49822.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022643-31371.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022643-36269.gif)
A.不存在 | B.有且只有一对 |
C.有且只有两对 | D.有无数对 |
(Ⅰ)求证:DM//平面APC;
(Ⅱ)求证:BC⊥平面APC;
(Ⅲ)若BC=4,AB=20,求三棱锥D—BCM的体积.
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