题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010646-93418.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010646-17269.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010646-63434.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010646-46085.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010646-61605.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010647-99758.png)
(Ⅰ) 证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010647-30254.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010647-49665.png)
(Ⅱ)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010647-33489.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010648-36284.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010648-68783.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010648-86228.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010647-30254.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010648-57610.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010648-57610.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010648-42293.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010647-49665.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010649-30822.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010647-49665.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010647-30254.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010647-49665.png)
(Ⅱ)连接
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010649-95206.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010646-17269.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010649-44075.png)
所以四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010649-52764.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010650-98363.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010647-30254.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010648-57610.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010650-60168.png)
又因为
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010650-37677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010650-98601.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010651-76996.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010651-34823.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010651-64653.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010651-34823.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010651-64653.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010651-19095.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010647-33489.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010648-36284.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010651-83375.png)
解析
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010633-99926.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010634-61402.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010634-77517.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010634-51173.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010634-32277.jpg)
(I)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010635-55987.jpg)
(II)当
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010635-36105.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010635-53292.jpg)
(III) 在(II)条件下求P到平而AMN的距离.
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010635-69931.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010611-58682.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010611-79337.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010612-83630.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010612-23213.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010612-99973.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010612-57434.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010613-49046.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010613-67854.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010613-82228.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010613-61026.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010614-91803.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010614-80727.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010614-44780.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010614-70226.png)
(2)设点
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010615-36642.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010615-83316.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010615-88298.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010615-83535.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010615-74835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010616-89353.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010616-27315.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010559-82763.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010559-31429.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010559-76087.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010600-14286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010600-72724.png)
且
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010600-99130.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010600-53396.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010601-41048.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010601-89729.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010601-59918.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010549-60234.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010549-43081.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010549-30683.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010549-40304.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010549-41501.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010549-43724.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010549-87408.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010549-31861.png)
(1)证明:面
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010550-41057.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010550-39006.png)
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010550-25296.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010549-31861.png)
(3)求面
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010550-54392.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010550-81855.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010550-26269.jpg)
(Ⅰ)求证:AE⊥PD;
(Ⅱ)若直线PB与平面PAD所成角的正弦值为
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010536-80700.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010536-30884.png)
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