题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062639-28818.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062639-20060.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062639-41960.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062639-21337.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062639-80015.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062639-70547.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062640-26499.png)
(Ⅰ)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062640-87057.png)
(Ⅱ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062640-22402.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062640-87810.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062640-60633.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062640-12305.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062640-99616.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062640-98780.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062641-89544.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062640-99616.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062641-80810.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062641-54087.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062641-47306.png)
解:(Ⅱ)建立如图所示空间直角坐标系
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062641-44302.png)
由已知可得
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062642-75443.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062642-96685.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062642-38086.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062642-75691.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062642-26238.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062643-88095.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062642-96685.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062643-78100.png)
解析
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062629-15638.jpg)
①水的部分始终呈棱柱状; ②水面四边形EFGH的面积不改变;
③棱A1D1始终与水面EFGH平行; ④当容器倾斜如图乙时,BE·BF是定值
其中正确说法是 ( )
A.①②③ | B.①③ | C.①②③④ | D.①③④ |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062623-82372.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062623-58566.png)
A.若![]() | B.若![]() |
C.若![]() | D.若![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062614-89140.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062614-89876.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062614-49697.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062614-66682.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062615-93869.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062615-49913.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062615-54869.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062614-66682.png)
(1)求异面直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062615-71067.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062615-40423.png)
(2)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062616-12857.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062616-84222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062608-31147.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062608-74035.png)
①若
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062608-84779.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062609-42349.png)
③若
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062609-93952.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062609-83504.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062609-75405.png)
则上述命题中正确的是( )
A.①② | B.②③ | C.③④ | D.①④ |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062538-32439.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062538-85754.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062538-65068.png)
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062538-30128.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062539-28112.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022062539-30407.png)
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