题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035940-80753.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035941-89732.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035941-66789.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035941-83217.png)
(I)求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035942-19779.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035942-84221.png)
(II)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035942-72062.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035942-23501.png)
(III)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035943-20508.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035943-29797.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035943-34386.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035943-18488.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035944-79082.png)
(1)证明:由直三棱柱性质,B1B⊥平面ABC,
∴B1B⊥AC,
又BA⊥AC,B1B∩BA=B,
∴AC⊥平面 ABB1A1,
又AC
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035944-54169.png)
∴平面B1AC⊥平面ABB1A1.
(2)解:过A1做A1M⊥B1A1,垂足为M,连结CM,
∵平面B1AC⊥平面ABB1A,且平面B1AC∩平面ABB1A1=B1A,
∴A1M⊥平面B1AC.
∴∠A1CM为直线A1C与平面B1AC所成的角,
∵直线B1C与平面ABC成30°角,
∴∠B1CB=30°.
设AB=BB1=a,可得B1C=2a,BC=
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035944-12312.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035944-24016.png)
∴直线A1C与平面B1AC所成角的正弦值为
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035943-34386.png)
(3)解:过A做AN⊥BC,垂足为N,过N做NO⊥B1C,垂足为O,连结AO,
由AN⊥BC,可得AN⊥平面BCC1B1,由三垂线定理,可知AO⊥B1C,
∴∠AON为二面角B—B1C—A的平面角,
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035945-83338.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035918-41371.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035918-32886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035918-26339.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035919-70349.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035919-37534.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035919-83961.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035920-92751.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035920-72411.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035920-70912.png)
(Ⅰ)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035920-26105.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035921-87080.png)
(Ⅱ)求异面直线
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035921-76727.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035921-22386.png)
(Ⅲ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035919-70349.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035922-32580.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035922-84778.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035911-74761.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035912-23344.png)
(1)求证:AM⊥平面A1BC;
(2)求二面角B—AM—C的大小;
(3)求点C到平面ABM的距离。
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035908-75142.png)
A.一定是异面 | B.一定是相交 | C.不可能平行 | D.可能相交 |
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035904-76644.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035904-56491.png)
A.![]() ![]() ![]() |
B.直线![]() ![]() ![]() ![]() |
C.直线![]() ![]() |
D.![]() ![]() ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035856-16864.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035857-32781.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035857-93990.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106035857-32781.png)
A.只有一条,不在![]() | B.有无数条,不一定在![]() |
C.只有一条,且在![]() | D.有无数条,一定在![]() |
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