题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044530-32151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044531-52762.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044531-32478.png)
(1)求证:BD
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044531-97218.png)
(2)求异面直线BC与PD所成的角.
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044531-22151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044531-96510.png)
(2)45º.
解析
试题分析:(1)
证明:∵
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044531-59378.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044531-79710.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044531-22151.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044531-52762.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044531-96510.png)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044531-50057.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044531-93445.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044532-73248.png)
(2)解: ∵
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044531-52762.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044532-42240.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044532-47715.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044532-54315.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044532-75912.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044532-47715.png)
由已知可知,△
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044533-59630.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044533-73603.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044533-14913.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044533-24319.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044533-81369.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044532-75912.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044532-47715.png)
点评:主要是考查了空间中线面的垂直的证明,以及异面直线所成的角的求解,属于基础题。
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044519-16356.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044519-48493.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044519-12458.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044519-94463.png)
A.![]() ![]() ![]() | B.![]() ![]() ![]() ![]() ![]() ![]() |
C.![]() ![]() ![]() ![]() | D.![]() ![]() ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044504-96833.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044505-79120.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044505-72076.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044505-59413.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044505-24863.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044505-84217.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044506-36909.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044506-52824.png)
(2)求证;
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044506-19983.png)
(3)求三棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044506-57977.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044457-88982.png)
(1)求证:AD⊥PB;
(2)求异面直线PD与AB所成角的余弦值;
(3)求平面PAB与平面PCD所成锐二面角的大小.
A.直线上至少有一个点在平面内 |
B.直线上有无穷多个点在平面内 |
C.直线上所有点都在平面外 |
D.直线上至多有一个点在平面内 |
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