题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031924-81303.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031924-38452.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031925-10084.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031925-33468.png)
(Ⅰ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031925-19474.png)
(Ⅱ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031925-54116.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031926-59406.png)
(Ⅲ)求异面直线
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031926-14245.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031926-20699.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031926-90685.jpg)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031927-89110.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031927-77560.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031927-11685.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031927-24761.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031928-62070.png)
(II)连接BC1交B1C交于O点,连接OD,则OD//AC1,所以
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031925-54116.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031926-59406.png)
(III)在(I)的基础上可知
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031928-21073.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031926-14245.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031926-20699.png)
(Ⅰ)∵直三棱柱ABC—A1B1C1中
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031928-99329.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031928-40070.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031928-67024.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031929-65792.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031929-88527.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031925-19474.png)
(Ⅱ)设CB1与C1B的交点为E,连结DE,…………….5
∵D是AB的中点,E是BC1的中点,
∴DE//AC1,…………………………………………7
∵DE
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031929-91031.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031930-45236.png)
∴AC1//平面CDB1……………………………………9
(Ⅲ)∵DE//AC1,∴∠CED或其补角为AC1与B1C所成的角……..10
在△CED中,ED
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031930-99533.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031930-31706.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031930-40652.png)
∴异面直线AC1与B1C所成角的余弦值为
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031927-89110.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031917-96302.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031918-69548.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031918-64626.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031918-53620.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031919-23387.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031917-96302.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031919-19541.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031919-29034.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031919-13030.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031920-30641.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031920-85602.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031920-35028.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031920-43865.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031921-43967.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031915-36685.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031911-56343.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031911-56343.png)
A.b![]() ![]() | B.b与平面![]() |
C.b∥平面![]() | D.b在平面![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031906-55678.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031906-87765.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031907-45897.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031907-56851.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031907-45760.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031858-54007.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031858-12383.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031858-57553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031859-36445.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031859-52584.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031859-75931.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031859-59549.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031900-25485.png)
(2)平面
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031900-47159.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031900-80490.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106031900-59119.png)
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