题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004537-75168.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004537-21602.png)
(2)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004537-48310.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004538-20207.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004538-36349.png)
解析
试题分析:由已知四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004538-53317.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004538-59230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004538-49831.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004538-13458.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004539-89270.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004538-13458.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004539-81899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004539-81899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004539-14769.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004539-10905.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004539-29259.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004540-23845.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004540-38016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004540-14112.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004540-57953.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004541-10848.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004541-36323.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004541-23191.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004541-68567.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004541-85616.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004542-74391.png)
试题解析:∵四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004538-53317.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004542-38018.png)
∵平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004538-49831.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004538-13458.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004539-89270.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004538-13458.png)
∴可以以点
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004539-81899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004539-81899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004539-14769.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004539-10905.png)
分别以直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004539-29259.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004540-23845.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004540-38016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004540-14112.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004540-57953.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004542-35134.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004542-38258.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004542-41263.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004543-43039.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004538-53317.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004543-96142.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004543-80617.png)
(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004543-18208.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004544-17744.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004544-28927.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004544-28415.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004544-44094.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004544-72245.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004545-77646.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004545-83926.png)
(2) 设平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004545-75703.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004541-68567.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004541-85616.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004542-74391.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004545-66917.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004545-65825.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004546-80473.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004546-67822.png)
取
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004546-85085.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004546-94319.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004546-95839.png)
又∵
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004547-89197.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004547-52273.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004547-96687.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004547-25521.png)
设二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004548-65464.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004548-65255.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004548-11137.png)
∴二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004548-65464.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004538-36349.png)
(1) ,(2)均可用几何法
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004530-42296.png)
(1)求证:AN∥平面 MBD;
(2)求异面直线AN与PD所成角的余弦值;
(3)求二面角M-BD-C的余弦值.
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