题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022611-39038.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022611-29426.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022612-50781.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022612-77361.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022612-12686.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022612-36676.png)
(2)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022613-64202.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022613-47667.png)
解析
试题分析:(1)要证线线垂直,一般通过证明线面垂直来实现,那么我们就要寻找图形中已有哪些与待证线垂直的直线,本题中首先由已知有
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022613-12403.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022613-51105.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022612-50781.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022614-60773.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022614-60985.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022614-11503.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022615-64745.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022615-12132.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022615-12132.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022615-96061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022615-63285.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022616-76769.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022616-89840.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022615-12132.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022615-12132.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022616-40378.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022616-73234.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022617-69985.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022617-97643.png)
试题解析:(1)连接BD,∵
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022611-29426.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022612-50781.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022617-37158.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022612-50781.png)
∴AC⊥SD 4分
又四边形ABCD是正方形,∴AC⊥BD
∴AC ⊥平面SBD
∴AC⊥SB. 6分
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022617-24273.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022615-12132.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022616-40378.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022618-66661.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022618-32473.png)
∵SD=AD,CS=CA,
∴DE⊥SA, CE⊥SA.
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022617-97643.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022613-64202.png)
计算得:DE=
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022618-16845.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022618-88619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022619-26690.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022619-21886.png)
所以所求二面角的大小为
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022613-47667.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022605-27890.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022605-86532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022606-51279.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022606-47442.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022606-96518.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022606-47442.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022606-51279.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022606-96518.png)
②若
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022606-51279.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022606-47442.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022606-67804.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022606-26134.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022607-86897.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022606-51279.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022607-72400.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022607-11282.png)
其中正确的个数是 ( )
A.0 | B.1 | C.2 | D.3 |
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022551-12167.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022551-18136.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022551-17802.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022551-12204.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022551-17802.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022551-74913.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022551-11427.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022551-16192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022552-78604.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022552-10493.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022552-35364.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022552-70371.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022552-65077.png)
其中正确的命题的序号是
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022552-25002.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022539-32140.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022540-87694.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022540-28627.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022540-87694.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022540-20490.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022540-92034.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022541-19832.png)
求证:(I)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022541-98133.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022541-50473.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022541-27767.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022542-94196.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022525-38628.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022525-40171.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022525-84678.png)
(Ⅰ)求证:AC1⊥平面A1BC;
(Ⅱ)求平面AA1B与平面A1BC的夹角的余弦值。
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022504-20221.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022504-74443.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022504-15959.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022504-61243.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022504-74443.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022504-36880.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022505-52718.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022505-18452.png)
求证:(Ⅰ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022504-36880.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022505-52718.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022505-12670.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022506-44278.png)
(Ⅱ)无论
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022504-36880.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022505-52718.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022506-44728.png)
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