题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231728-69830.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231729-67890.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231729-78914.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231729-28257.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231729-96350.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231729-95801.jpg)
(Ⅰ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231730-49940.png)
(Ⅱ)求三棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231730-89114.png)
(Ⅲ)在线段
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231730-29998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231730-55124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231731-93810.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231731-58076.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231729-96350.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231731-39614.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231731-63402.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231732-28189.png)
(3)在线段
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231730-29998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231730-55124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231731-93810.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231732-27016.png)
解析
试题分析:解:(Ⅰ)∵平面
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231729-96350.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231732-36741.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231731-39614.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231731-63402.png)
又∵
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231732-26286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231730-49940.png)
(Ⅱ)如图(1)在
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231733-35473.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231733-50863.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231733-33096.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231733-54564.png)
如图(2),在
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231733-16719.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231734-59580.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231734-64724.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231734-83850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231734-69937.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231735-69167.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231735-94473.png)
(Ⅲ)在线段
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231730-29998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231730-55124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231731-93810.png)
如图(2)在
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231735-34029.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231735-82173.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231736-64304.png)
过点E做
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231736-91920.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231730-29998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231736-61087.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231736-82561.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231734-64724.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231736-88270.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231737-56889.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231737-32502.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231737-77385.png)
∴在线段
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231730-29998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231730-55124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231731-93810.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231732-27016.png)
点评:本小题主要考查直线与直线、直线与平面的位置关系、棱锥体积公式等基础知识,考查空间想象能力、推理论证能力及运算求解能力,考查化归与转化思想、数形结合思想
核心考点
试题【在直角梯形ABCD中,AD//BC,,,如图(1).把沿翻折,使得平面,如图(2).(Ⅰ)求证:;(Ⅱ)求三棱锥的体积;(Ⅲ)在线段上是否存在点N,使得?若存在】;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/20191020/20191020231723-67395.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231723-90052.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231723-11700.png)
(1)求证:AE
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231723-90052.png)
(2)求证:AE//平面BFD
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231711-89916.jpg)
(Ⅰ)求PD与BC所成角的大小;
(Ⅱ)求证:BC⊥平面PAC;
(Ⅲ)求二面角A-PC-D的大小.
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231700-53303.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231700-89303.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231700-31156.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231700-53303.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231701-99503.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231701-68235.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231701-31958.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231701-10592.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231702-22344.jpg)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231702-35829.png)
(2)求三棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231702-26854.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231638-97869.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231638-26638.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231639-97399.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231639-42314.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231639-10492.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231639-84792.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231640-11025.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231640-27254.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231640-51326.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231640-44066.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231641-77960.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231641-80868.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231641-96029.png)
(Ⅰ) 证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231641-45678.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231641-91393.png)
(Ⅱ) 求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231642-13434.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231624-16009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231624-23285.jpg)
(I)求证
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231625-67020.png)
(II)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231625-67610.png)
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