题目
题型:不详难度:来源:
(Ⅰ)证明:MN∥平面PCD;
(Ⅱ)求MN与平面PAC所成角的正切值.
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072910-15042.gif)
答案
∵M, N分别为PA, BC的中点,
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072910-46683.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072910-17882.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072910-68254.gif)
∴MNCE是平行四边形,∴MN∥CE,……………2分
∵CEÍ平面PCD,MNË平面PCD,
∴MN∥平面PCD.…………………………………2分
(Ⅱ)作NF⊥AC于F,连接MF.
∵PA⊥平面ABCD,∴PA⊥NF,又∵PA∩AC=A,
∴NF⊥平面PAC,∴∠FMN是MN与平面PAC所成的角.………2分
在Rt△MFN中,
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072911-77020.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072911-45338.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072911-12938.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072911-25352.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072912-45504.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072912-60853.gif)
解析
核心考点
试题【如图,在四棱锥P-ABCD中,PA⊥底面ABCD,底面ABCD为正方形,PA=AB=2,M, N分别为PA, BC的中点.(Ⅰ)证明:MN∥平面PCD;(Ⅱ)求】;主要考察你对线线角等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072903-74052.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072903-42374.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072903-74052.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072903-42374.png)
A.可能是平行直线 | B.一定是异面直线 | C.可能是相交直线 | D.平行、相交、异面直线都有可能 |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072856-71793.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072856-76518.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072856-72332.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072856-88524.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072856-71793.png)
A
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072857-99047.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072857-46586.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072857-29193.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072857-21988.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072858-80270.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072849-62801.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072849-90913.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072850-81021.gif)
与
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072850-30107.gif)
(Ⅰ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072850-24005.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072850-81656.gif)
(Ⅱ)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072851-80775.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072851-79560.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072843-88470.gif)
(1)求证:平面PCE
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072843-88519.gif)
(2)设M、N分别为棱PA、EC的中点,求直线MN与平面PAE所成角的正弦;
(3)求二面角A-PE-C的大小。
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072843-75416.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072843-23766.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072837-55834.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072837-21480.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072838-94157.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072838-72054.png)
(1)求证:EF
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072838-98134.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072838-53943.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072838-93655.png)
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