题目
题型:不详难度:来源:
如图,已知
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014400-11660.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014400-57993.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014400-23940.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014401-83114.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014401-77253.gif)
(Ⅰ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014401-64111.gif)
(Ⅱ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014401-98611.gif)
(Ⅲ)求三棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014401-97978.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014402-43805.jpg)
答案
解析
(Ⅰ)证明:取
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014402-27351.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014402-57284.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014402-80768.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014402-90103.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014403-77449.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014403-84331.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014403-10261.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014403-64816.gif)
又∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014404-50980.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014404-69640.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014404-33585.gif)
∴四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014404-10532.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014404-26861.gif)
又∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014405-32808.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014405-27643.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014405-61794.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014405-27643.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014405-34740.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014405-27643.gif)
(Ⅱ)证明:∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014405-24357.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014406-30113.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014406-25466.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014406-30113.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014406-21049.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014406-30113.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014405-24357.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014406-54797.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014405-24357.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014407-27127.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014407-69042.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014407-68737.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014407-10241.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014405-27643.gif)
又∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014405-61794.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014405-27643.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014407-10241.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014408-46295.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014408-32849.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014402-57284.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014402-27351.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014408-98852.gif)
又∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014408-44274.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014408-66654.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014408-26204.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014404-26861.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014409-91559.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014408-26204.gif)
又∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014409-47423.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014409-16307.gif)
∴平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014409-16307.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014409-69008.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014408-26204.gif)
(Ⅲ)解:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014410-31754.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014410-16569.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014410-33825.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014410-72734.gif)
核心考点
试题【(本题满分12分)如图,已知所在的平面,分别为的中点,,(Ⅰ)求证:; (Ⅱ)求证:;(Ⅲ)求三棱锥的体积.】;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
如图,在四棱锥S—ABCD中,已知底面ABCD为直角梯形,其中AD//BC,
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014356-92952.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014356-62927.gif)
(Ⅰ)在棱SD上找一点E,使CE//平面SAB,
并证明。
(Ⅱ)求二面角B—SC—D的余弦值。
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014356-14496.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014347-98433.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014347-83324.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014347-31325.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014347-33336.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014348-70192.gif)
(Ⅰ) 求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014348-95077.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014348-96514.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014348-95077.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014348-89970.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014348-38699.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014349-56963.gif)
在棱长为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014335-89762.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014335-50545.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014335-68029.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014336-89229.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014336-51177.gif)
(Ⅰ) 求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014336-48464.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014336-21154.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014336-48464.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014336-29197.gif)
(Ⅲ) 求三棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014337-12413.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014337-57986.gif)
①求证:EF⊥平面PCD;
②求平面PCB与平面PCD的夹角的余弦值.
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014320-89851.jpg)
如图,平行四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014310-23731.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014310-75288.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014311-20978.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014311-61143.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014311-69076.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014310-23731.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014311-70027.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014312-43057.gif)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014312-41267.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014312-62508.gif)
(2)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014312-95843.gif)
(3)求三棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014312-71278.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021014313-89897.gif)
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