题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121216-40678.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121216-52514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121216-54409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121216-31156.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121216-61672.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121216-17418.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121216-70103.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121216-41824.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121217-15123.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121217-16330.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121217-91708.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121216-40678.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121217-87817.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121217-13655.png)
解析
试题分析:(1)由
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121216-17418.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121218-21824.png)
(2)由平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121216-52514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121216-54409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121216-31156.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121216-61672.png)
(3)由
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121216-17418.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121217-16330.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121217-91708.png)
(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121218-52693.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121218-34906.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121218-87142.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121218-65131.png)
(2)因为平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121216-52514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121216-54409.png)
且平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121219-71143.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121219-49420.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121219-63276.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121219-16926.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121220-34629.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121220-31565.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121216-54409.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121220-56517.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121220-65361.png)
所以平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121216-52514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121216-54409.png)
(3)由(2)可知
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121220-31565.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121216-54409.png)
法一:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121220-92495.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121221-77842.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121221-73601.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121221-48819.png)
由正弦定理
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121221-82529.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121222-14280.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121222-91333.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121222-36938.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121222-35436.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121222-53006.png)
△
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121223-44356.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121223-95539.png)
所以三棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121216-40678.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121223-84830.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121223-49480.png)
法二:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121220-92495.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121224-11870.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121217-91708.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121221-48819.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121224-76539.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121224-37297.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121224-15526.png)
△
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121223-44356.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121224-88363.png)
所以三棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121216-40678.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121223-84830.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121223-49480.png)
核心考点
举一反三
(1)求证:DC∥平面PAB;
(2)求四棱锥P﹣ABCD的体积.
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121210-50533.png)
A.6π | B.4π | C.2π | D.π |
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121202-63368.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121202-89138.jpg)
A.4 | B.2 | C.2 | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121156-94324.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121150-24501.jpg)
(1)求证:GH∥平面CDE;
(2)若CD=2,DB=4
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121150-23212.png)
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