题目
题型:不详难度:来源:
如图,在四棱台
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045833-36218.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045833-29539.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045834-82116.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045834-14577.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045834-19321.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045833-29539.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045834-33246.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045834-61663.png)
(Ⅰ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045835-81248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045835-64258.png)
(Ⅱ)求平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045835-47039.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045835-26942.png)
答案
(Ⅰ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045836-74772.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045836-28005.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045836-14286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045835-81248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045835-64258.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045836-66437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045836-45468.png)
解析
试题分析:以D为原点,以DA、DC、DD1所在直线分别为x轴,z轴建立空间直角坐标系D—xyz如图,则有A(2,0,0),B(2,2,0),C(0,2,0),A1(1,0,2),B1(1,1,2),C1(0,1,2),D1(0,0,2). 3分
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045837-74934.png)
(Ⅰ)证明:设
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045836-74772.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045836-28005.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045836-14286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045837-85120.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045837-30082.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045835-81248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045835-64258.png)
(Ⅱ)解:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045837-35811.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045837-30889.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045838-88733.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045838-98586.png)
于是
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045838-35964.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045838-29448.png)
同理可以求得平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045835-64258.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045839-75299.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045839-38939.png)
∴二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045836-66437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045836-45468.png)
点评:典型题,立体几何题,是高考必考内容,往往涉及垂直关系、平行关系、角、距离、体积的计算。在计算问题中,有“几何法”和“向量法”。利用几何法,要遵循“一作、二证、三计算”的步骤。在空间垂直关系明确的情况下,通过建立适当的空间直角坐标系,利用向量可简化证明过程。本题难度不大。
核心考点
试题【用平行于棱锥底面的平面去截棱锥,则截面与底面之间的部分叫棱台。如图,在四棱台中,下底是边长为的正方形,上底是边长为1的正方形,侧棱⊥平面,.(Ⅰ)求证:平面;(】;主要考察你对线线角等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045829-27936.png)
A.若![]() ![]() | B.若![]() ![]() |
C.若![]() ![]() | D.若![]() ![]() |
A.8![]() | B.16![]() | C.14![]() | D.18![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045820-55316.jpg)
(1)求证:NC∥平面MFD;
(2)若EC=3,求证:ND⊥FC;
(3)求四面体NFEC体积的最大值.
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045813-23438.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045813-79471.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045813-93727.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045813-79586.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045814-37344.png)
(Ⅰ)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045814-11934.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045814-96854.png)
(Ⅱ)证明:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045814-99720.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045814-27389.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045802-45780.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045802-74383.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045803-71720.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045803-58875.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045802-74383.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045803-78030.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045803-50363.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045803-10797.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045804-34848.jpg)
(Ⅰ)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045804-54165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045804-26432.png)
(Ⅱ)求三棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022045804-14409.png)
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