题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030057-91973.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030057-64588.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030058-61004.png)
(2)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030058-70297.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030058-11393.png)
解析
试题分析:(1)先根据正方形的特征得到
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030058-19560.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030059-90293.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030059-90508.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030059-39853.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030059-54634.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030100-48950.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030100-75356.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030100-50806.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030100-47265.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030101-21739.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030101-40308.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030101-83126.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030101-93613.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030058-70297.png)
试题解析:(1)证明:∵
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030102-47767.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030058-19560.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030059-90293.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030059-90508.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030059-39853.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030102-29130.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030059-54634.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030102-87691.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030100-48950.png)
(2)取
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030100-75356.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030100-50806.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030100-47265.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030101-21739.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030103-57616.jpg)
则在
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030103-12515.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030103-34928.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030103-64780.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030101-40308.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030104-32846.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030101-83126.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030101-93613.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030058-70297.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030104-75559.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030104-33418.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030104-79395.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030105-54579.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030105-63569.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030059-54634.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030105-71368.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030105-19167.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030106-24574.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030106-41666.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030106-20560.png)
所以二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030058-70297.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030058-11393.png)
核心考点
试题【如图,边长为2的正方形ABCD,E,F分别是AB,BC的中点,将△AED,△DCF分别沿DE,DF折起,使A,C两点重合于.(1)求证:⊥EF;(2)求二面角的】;主要考察你对向量与空间位置关系等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030048-65329.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030048-76098.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030048-28325.png)
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030049-92632.png)
①若m∥n,n⊂α,则m∥α;
②若m⊥n,m⊥α,n
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030041-85322.png)
③若α⊥β,m⊥α,n⊥β,则m⊥n;
④若m,n是异面直线,m⊂α,n⊂β,m∥β,则n∥α.
其中正确的命题有( )
A.①② | B.②③ | C.③④ | D.②④ |
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030035-48787.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030035-96611.png)
①若
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030035-73744.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030036-90514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030036-64227.png)
②若
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030036-63201.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030036-64227.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030036-90514.png)
③若
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030036-61161.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030036-22113.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030036-90514.png)
④若
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030037-73420.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030037-98075.png)
其中真命题的个数是( )
A.4 | B.3 | C.2 | D.1 |
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030028-66083.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030028-76417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030029-75989.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030029-68069.jpg)
A.![]() ![]() ![]() ![]() ![]() |
B.![]() ![]() ![]() ![]() ![]() |
C.![]() ![]() ![]() ![]() ![]() |
D.![]() ![]() ![]() ![]() ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030014-91577.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030014-54595.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030014-20796.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030015-51237.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030015-42675.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030015-57145.jpg)
(1)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030015-10774.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106030016-86132.png)
(2)平面MNC与平面MAC夹角的余弦值.
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