题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045007-15114.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045007-50223.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045008-75188.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045008-84961.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045008-19941.jpg)
(Ⅰ) 求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045008-63021.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045008-85295.png)
(Ⅱ) 当
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045009-23271.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045009-57603.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045008-75188.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045009-10213.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045009-43127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045009-50019.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045010-97935.png)
解析
试题分析:(Ⅰ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045010-77761.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045010-77514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045010-25394.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045011-52482.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045011-87589.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045009-43127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045009-50019.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045011-40248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045011-19263.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045011-82283.png)
(Ⅱ)(方法一)根据题意,由于当
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045009-23271.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045009-57603.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045012-74203.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045012-65249.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045009-23271.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045012-38546.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045010-97935.png)
另解:(Ⅰ)设AC交BD于O,连接OE,∵PD⊥平面ABCD,∴PD⊥AC,∵BD⊥AC,∴AC⊥平面PBD,
又∵AC⊆平面AEC,∴平面ACE⊥平面PBD.…(6分)(Ⅱ)(方法一)∵平面ACE⊥平面PBD,∴AO⊥PBD,
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045012-33616.png)
∵直线AE与平面PBD成角为45°,∴∠AEO=45°,设PD=
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045013-31236.png)
点评:主要是考查了空间中面面垂直以及几何体的体积的公式的运用,属于中档题。
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045003-39575.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045003-53084.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045003-67377.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045003-18430.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045004-18890.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045004-10471.png)
PA=BC=1,PD=AB=
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044948-11874.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044949-93621.png)
(Ⅰ) 求证:CE∥平面PAF;
(Ⅱ)在线段BC上是否存在一点G,使得平面PAG和平面PGC所成二面角的大小为60°?若存在,试确定G的位置;若不存在,请说明理由.
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044940-31240.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044940-19215.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044940-29720.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044940-52484.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044940-53373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044940-89855.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044940-80588.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044941-88225.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044941-18212.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044941-20310.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044910-29585.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044910-12919.jpg)
(Ⅰ)证明:BC丄AB1;
(Ⅱ)若OC=OA,求二面角C1-BD-C的余弦值.
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044900-27719.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044900-43060.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044901-85516.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044901-52739.jpg)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044901-19371.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044901-17333.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044901-19371.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044902-32129.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044902-35611.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044902-45408.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022044902-71442.png)
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