题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010031-63768.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010031-91918.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010031-81430.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010032-97901.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010032-16709.gif)
(Ⅰ)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010032-32277.gif)
(Ⅱ)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010032-17641.gif)
答案
(Ⅰ)证明:设
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010032-99850.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010033-15930.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010033-13153.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010033-43693.gif)
在正三棱柱中,
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010033-84428.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010034-93499.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010034-52359.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010033-43693.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010034-80751.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010034-52359.gif)
易知
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010034-29316.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010034-18218.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010035-76864.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010035-87806.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010035-73530.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010035-28692.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010036-25336.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010032-32277.gif)
(Ⅱ)由(Ⅰ)知
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010036-16718.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010036-49781.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010036-96149.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010036-93366.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010037-89678.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010037-58613.gif)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010037-76157.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010032-17641.gif)
不妨设
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010037-50488.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010038-33825.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010038-39925.gif)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010038-42406.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010038-15255.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010039-37826.gif)
方法二:
(Ⅰ)在正三棱柱中,以
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010033-15930.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010032-99850.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010039-49115.gif)
不妨设
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010037-50488.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010039-37532.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010039-45467.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010039-48966.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010040-43462.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010040-48621.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010040-82659.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010040-27891.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010032-32277.gif)
(Ⅱ)在空间直角坐标系
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010039-49115.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010040-42121.gif)
易知平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010036-49781.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010041-35019.gif)
设平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010041-98643.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010041-61437.gif)
易知
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010041-43238.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010040-82659.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010042-75508.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010042-49244.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010042-16768.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010042-94201.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010042-64580.gif)
∴二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010032-17641.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010043-23486.gif)
解析
核心考点
试题【如图,正三棱柱中,,是侧棱的中点.(Ⅰ)证明:;(Ⅱ)求二面角的大小.】;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/20191021/20191021010018-59471.gif)
(Ⅰ)求证:BD⊥平面PAC;
(Ⅱ)求点C到平面PBD的距离.
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010018-66182.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010003-84366.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010003-92486.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010003-70116.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010004-52785.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010004-62675.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010004-22801.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010004-85884.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021010005-98485.gif)
A.
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021005956-76743.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021005956-73356.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021005956-58447.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021005956-17671.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021005957-23269.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021005951-62463.gif)
A.-a+![]() | B.a-b+c | C.a+b-c | D.a+b-c |
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021005946-10907.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021005946-95702.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021005946-73122.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021005946-46993.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021005947-54179.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021005947-61118.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021005947-87496.gif)
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