题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010746-51159.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010746-89770.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010746-97967.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010746-97967.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010746-51171.png)
(Ⅰ)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010747-54129.png)
(Ⅱ)若棱
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010747-30466.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010747-78240.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010747-54835.png)
当二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010747-62769.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010747-93098.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010747-75764.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010748-89419.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010748-23639.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010748-23892.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010748-36848.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010748-47151.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010749-94605.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010749-93046.png)
(Ⅰ)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010749-36740.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010749-63601.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010747-54129.png)
(Ⅱ)∵
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010747-54835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010750-23550.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010750-45029.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010750-40640.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010750-92293.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010750-29066.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010751-30593.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010751-82216.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010751-95523.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010751-45852.png)
设平面
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010752-73427.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010752-42306.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010752-87012.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010752-63197.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010753-40274.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010753-38183.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010753-17326.png)
解析
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010737-55412.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010737-74871.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010737-55888.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010738-73241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010738-32228.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010738-67841.png)
(Ⅰ) 图
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010737-55412.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010738-99451.png)
(Ⅱ)求正三棱柱
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010737-74871.png)
(Ⅲ)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010739-41477.png)
(1)求证:MN//A1C1;
(2)求:异面直线MN与BC1所成角的余弦值.
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010729-17226.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010722-89950.png)
(1)求证:EF//平面PAD;
(2)求证:EF
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010722-89950.png)
(3)求:直线BD与平面EFC所成角的大小.
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010722-13044.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010712-51783.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010712-80111.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010712-79082.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010712-80111.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010712-62834.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010712-97289.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010712-37577.png)
(1)证明
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010713-26046.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010713-47781.png)
(2)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010713-13234.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010713-30345.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010654-29764.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010655-85688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010655-21236.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010655-85688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010655-29866.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010655-15750.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010656-55747.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010656-70778.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010656-16235.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010656-47747.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010656-84894.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010657-72239.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010657-87317.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010657-92202.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010657-33337.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010657-24047.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010658-98906.png)
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