题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081503-53740.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081503-12265.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081503-42263.png)
(Ⅰ) 求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081504-13941.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081504-98514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081504-25137.png)
(Ⅲ)求三棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081504-19290.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081504-38287.png)
答案
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081504-12662.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081504-82957.png)
解析
(1)结合线面垂直的性质定理和判定定理的综合运用,求证线线垂直。
(2)利用线面平行的判定定理得到证明。
(3)先求解底面的面积,结合锥体的高,得到三棱锥体积。
解: (Ⅰ)证明:连结
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081504-99154.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081504-99154.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081505-93630.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081505-24013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081505-66104.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081505-56770.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081505-24013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081505-15536.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081506-11953.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081506-67178.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081506-66597.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081506-92057.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081506-66597.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081507-46033.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081507-10137.png)
(Ⅱ)证明:作
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081507-77599.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081507-58715.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081507-95970.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081508-95939.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081508-44753.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081508-94187.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081508-90015.png)
∴四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081508-93663.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081509-47280.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081509-43755.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081508-95939.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081509-95929.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081509-79544.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081510-47697.png)
∴四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081510-94443.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081510-94682.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081510-56988.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081510-32731.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081511-97344.png)
∴平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081511-39945.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081504-25137.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081511-31885.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081511-90975.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081504-98514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081504-25137.png)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081504-12662.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081504-82957.png)
核心考点
试题【(本小题满分14分)正方体,,E为棱的中点.(Ⅰ) 求证:; (Ⅱ) 求证:平面;(Ⅲ)求三棱锥的体积.】;主要考察你对空间几何体的视图与直观图等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081456-27967.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081457-89832.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081457-81403.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081457-99342.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081457-48165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081457-75349.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081451-62842.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081451-29023.png)
A.
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081452-23789.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081452-41936.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081452-94530.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081452-94530.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081443-80105.png)
A.![]() | B.2 | C.![]() | D.6 |
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081439-94075.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081435-91222.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081435-99755.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021081436-86187.jpg)
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