题目
题型:不详难度:来源:
如图,在直三棱柱
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025058-55001.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025059-84494.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025059-91857.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025059-99672.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025059-76412.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025059-50693.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025100-56963.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025100-33132.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025100-28410.gif)
(I)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025100-69695.gif)
(II)求
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025100-24009.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025101-97297.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025101-81410.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025101-70806.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025100-69695.gif)
(II)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025101-63798.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025101-76607.gif)
解析
∵三棱柱ABC-A,BC是直三棱柱.
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025102-94923.gif)
∴CD为C1D在平面ABC内的射影.
∵△ABC中,AC=BC,D为AB中点.
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025102-68147.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025102-97871.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025102-63244.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025102-45238.gif)
(Ⅱ)解法一:过点A作CE的平行线,交ED的延长线于F,连结MF.
∵D、E分别为AB、BC的中点.
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025102-81042.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025103-65075.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025103-88494.gif)
∵AF为MF在平面ABC内的射影,
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025103-17577.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025103-80314.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025103-17371.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025103-41011.gif)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025104-92465.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025104-15390.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025103-41011.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025101-63798.gif)
作
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025104-33514.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025104-47467.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025105-89884.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025105-25371.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025105-47140.gif)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025104-92465.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025103-41011.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025105-66297.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025105-66065.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025101-76607.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025106-94103.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025106-89430.gif)
∴C到平面MDE的距离与A到平面MDE的距离相等,为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025101-76607.gif)
解法二:过点A作CE的平行线,交ED的延长线于F,连结MF.
∵D、E分别为AB、CB的中点,
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025102-81042.gif)
又∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025103-65075.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025103-88494.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025106-84475.gif)
∴AF为MF在平面ABC内的射影,
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025103-17577.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025103-80314.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025103-17371.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025103-41011.gif)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025104-92465.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025104-15390.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025103-41011.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025101-63798.gif)
设C到平面MDE的距离为h.
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025106-63799.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025106-13439.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025107-81773.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025107-45210.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025107-74245.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025107-45572.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025101-76607.gif)
核心考点
试题【(本小题满分12分)如图,在直三棱柱中,,,分别为棱的中点,为棱上的点,二面角为.(I)证明:;(II)求的长,并求点到平面的距离.】;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/20191021/20191021025038-22133.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025038-18992.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025038-76283.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025038-85994.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025039-85945.png)
(Ⅰ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025039-28460.png)
(Ⅱ)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025039-58664.png)
则这三个平面把空间分成( )
A.5部分 | B.6部分 | C.7部分 | D.8部分 |
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025034-61726.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025001-43762.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025002-45108.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025002-79010.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025002-21431.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025002-16272.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025003-48042.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025003-40835.png)
(1)求异面直线DE与
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025003-89963.png)
(2)若BC =
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025003-92340.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025003-26147.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021024942-88671.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021024942-19353.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021024943-98263.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021024942-19353.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021024943-19195.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021024943-60185.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021024943-59354.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021024943-15657.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021024944-13525.png)
(I)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021024944-57733.png)
(II)求
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021024944-64790.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021024944-62857.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021024927-79637.gif)
如图,在
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021024927-31483.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021024927-87477.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021024927-72897.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021024927-64897.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021024927-31483.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021024927-91742.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021024927-73929.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021024928-56661.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021024928-10665.gif)
(I)求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021024928-89081.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021024928-74328.gif)
(II)当
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021024928-56661.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021024928-10665.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021024927-91742.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021024929-40039.gif)
(III)求
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021024929-40039.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021024928-74328.gif)
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