题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230334-81346.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230334-12784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230335-97583.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230334-12784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230335-36811.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230335-34580.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230335-55480.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230335-16650.png)
(1)证明平面
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230336-68033.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230336-57321.png)
(2)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230336-66996.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230336-37442.png)
解析
试题分析:(1) 由
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230337-95096.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230337-45025.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230337-98209.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230337-43167.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230337-89314.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230338-61526.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230338-61541.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230336-57321.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230336-68033.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230336-57321.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230338-13925.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230336-66996.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230338-50449.png)
试题解析:证明:(1) ∵
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230335-36811.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230335-34580.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230335-55480.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230339-11368.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230335-97583.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230334-12784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230337-95096.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230337-45025.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230339-18536.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230337-98209.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230337-43167.png)
所以有
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230337-89314.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230339-31490.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230338-61526.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230339-46784.png)
于是,由
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230340-21348.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230339-11368.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230338-61526.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230338-61541.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230336-57321.png)
故可得平面
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230336-68033.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230336-57321.png)
(2)取CD的中点F,连接AC与BD,交点为M,取DM的中点N,连接EN,FN,易知
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230338-13925.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230336-66996.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230340-40870.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230340-82735.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230340-61050.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230338-50449.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230341-42616.png)
所以二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230336-66996.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230336-37442.png)
核心考点
试题【如图,四棱锥的底面是正方形,棱底面,=1,是的中点.(1)证明平面平面; (2)求二面角的余弦值.】;主要考察你对空间几何体的结构特征等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230310-30524.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230310-62175.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230310-27175.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230310-60210.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230310-60726.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230311-52053.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230310-27175.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230311-75435.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230311-47413.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230311-91494.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230311-65760.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230311-29504.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230311-68078.png)
(1) 求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230312-78634.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230312-59539.png)
(2) 求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230312-98251.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230312-51943.png)
(3) 设
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230312-76895.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230311-52053.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230312-77142.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230312-89457.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230313-27007.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230313-13076.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230253-52475.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230253-87942.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230253-49767.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230253-88765.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230253-87942.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230253-64984.png)
(I) 证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230254-95586.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230253-49767.png)
(II)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230254-43009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230242-79240.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230242-79240.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230243-40417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230243-50886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230243-20884.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230244-39542.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230244-61284.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230244-25896.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230244-46851.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230245-10364.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230245-38055.png)
(2)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230245-10364.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230245-20346.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230227-80900.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230228-80176.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230228-25712.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230228-80176.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230228-88364.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230228-84079.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230228-42610.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230229-77021.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230229-20667.png)
(Ⅰ)证明
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230229-61031.png)
(Ⅱ)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230229-42032.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230229-38426.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230214-57323.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230214-34069.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230215-39074.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230215-46053.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230215-53469.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230215-39011.png)
(Ⅰ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230216-17882.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230216-17882.png)
(Ⅱ)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230216-25608.png)
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