题目
题型:不详难度:来源:
如图,四棱锥P—ABCD的底面ABCD为一直角梯形,其中BA⊥AD,CD⊥AD,CD=AD=2AB,PA⊥底面ABCD,E是PC的中点.
(Ⅰ)求证:BE//平面PAD;
(Ⅱ)若BE⊥平面PCD。
(i)求异面直线PD与BC所成角的余弦值;
(ii)求二面角E—BD—C的余弦值.
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022151-40790.jpg)
答案
(Ⅱ)(i)异面直线
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022151-88227.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022151-33288.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022151-28583.gif)
(ii)二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022151-37280.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022151-58672.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022151-75776.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022151-56306.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022151-34152.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022152-17471.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022152-57563.gif)
(Ⅰ)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022152-26414.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022152-21839.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022152-10766.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022152-91746.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022152-86750.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022152-84437.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022152-86750.gif)
(Ⅱ)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022152-14456.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022153-21522.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022153-66435.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022153-20212.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022153-26572.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022153-26276.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022153-14684.gif)
①
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022153-44544.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022154-67209.gif)
所以异面直线
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022151-88227.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022151-33288.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022151-28583.gif)
②平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022154-24220.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022154-64390.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022154-93258.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022154-22908.gif)
所以平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022154-24220.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022154-17124.gif)
平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022155-34049.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022155-11135.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022155-40413.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022151-37280.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022151-58672.gif)
核心考点
试题【(本题满分14分)如图,四棱锥P—ABCD的底面ABCD为一直角梯形,其中BA⊥AD,CD⊥AD,CD=AD=2AB,PA⊥底面ABCD,E是PC的中点.(Ⅰ)】;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/20191021/20191021022135-59060.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022135-48744.gif)
A.若![]() ![]() | B.若![]() ![]() |
C.若![]() | D.若![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022126-10321.gif)
(Ⅰ)证明:CD⊥平面PAC;
(Ⅱ)在线段PD上是否存在一点E,使得NM∥平面ACE;若存在,求出PE的长;若不存在,说明理由.
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022127-37189.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022119-89386.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022119-84081.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022119-71923.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022120-81140.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022120-10812.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022120-35828.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022120-56490.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022120-71445.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022121-33873.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022121-95779.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022121-94966.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022121-87746.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022122-88696.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022122-64536.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022122-39354.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022122-67949.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022122-63410.gif)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022107-81006.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022108-20782.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022108-44448.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022108-44448.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022054-63598.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022054-68580.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022054-17782.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022054-68580.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022054-55476.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022055-88609.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022055-68680.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022055-13745.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022055-25749.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022056-61841.gif)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022056-80597.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022056-94035.gif)
(2)求平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022056-94035.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022056-24498.gif)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022056-71450.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022057-59974.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022055-25749.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022057-95789.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022057-10663.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022056-94035.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022057-95789.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022057-94905.gif)
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