题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230923-19417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230923-72445.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230923-70057.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230923-54381.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230924-86256.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230924-29537.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230924-29909.png)
(Ⅰ)求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230924-15553.png)
(Ⅱ)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230925-12565.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230925-18058.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230925-67373.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230925-24437.png)
解析
试题分析:(Ⅰ)取
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230924-86256.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230925-85416.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230926-68167.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230924-15553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230926-81060.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230925-18058.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230926-14114.png)
试题解析:(Ⅰ)∵在矩形
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230923-19417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230923-72445.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230923-70057.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230923-54381.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230926-41774.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230927-82679.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230927-80684.png)
取
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230924-86256.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230927-52998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230927-62963.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230928-70723.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230928-67317.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230928-15403.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230928-92687.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230929-60409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230929-28027.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230929-68767.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230929-78558.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230930-24938.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230926-68167.png)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230930-29671.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230924-29537.png)
∴平面
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230924-29537.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230926-68167.png)
(Ⅱ)解:分别以直线
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230930-87976.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230930-87384.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230931-89729.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230931-42357.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230931-73641.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230931-19266.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230931-62266.png)
设平面
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230932-79195.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230932-21832.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230932-70325.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230932-46568.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230933-36269.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230933-55742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230933-14735.png)
取
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230933-17330.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230934-59856.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230925-12565.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230925-18058.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230934-46510.png)
即直线
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230925-12565.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230925-18058.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230934-90009.png)
核心考点
试题【如图,已知矩形中,为的中点,沿将三角形折起,使.(Ⅰ)求证:平面;(Ⅱ)求直线与平面所成角的正弦值.】;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/20191020/20191020230910-48294.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230910-24223.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230910-38175.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230911-66548.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230911-64077.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230911-55314.png)
(Ⅰ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230911-61051.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230911-27791.png)
(Ⅱ)求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230911-27791.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230912-68837.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230912-42326.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230912-85618.png)
A.0个 | B.1个 | C.2个 | D.3个 |
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230846-36422.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230846-79516.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230846-97762.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230846-97762.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230846-77975.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230846-29635.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230846-74206.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230847-77228.png)
(Ⅰ)求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230847-93854.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230847-35384.png)
(Ⅱ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230847-29604.png)
(ⅰ) 若直线
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230847-81428.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230847-22561.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230847-39958.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230847-33621.png)
(ⅱ) 在线段
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230847-36370.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230848-82090.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230848-82090.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230848-82321.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230848-58346.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230833-91783.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230833-39242.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230833-67444.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230833-29803.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230834-20068.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230833-29803.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230834-16456.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230834-92030.png)
(Ⅰ)证明:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230834-56168.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230834-45495.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230835-60521.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230835-90508.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230835-52344.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230818-70367.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230818-78695.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230818-79452.png)
(Ⅰ)判断直线EF与A¢D的位置关系,并说明理由;
(Ⅱ)求二面角F-A¢B-D的大小.
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