题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230124-64410.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230124-79629.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230124-94275.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230124-90030.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230124-83223.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230124-45368.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230124-33984.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230125-25193.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230124-79629.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230125-33815.png)
(Ⅰ)证明:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230125-87310.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230125-61063.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230125-64309.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230126-50094.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230126-37838.png)
(Ⅲ)在(Ⅱ)的条件下,试求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230126-34579.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230126-11524.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230127-75287.png)
解析
试题分析:(Ⅰ)证明面面垂直问题转化为证明线面垂直问题,即某一个平面中的某条直线垂直于另一个平面.然后将线面垂直问题转化为线线垂直问题,即该直线与平面中的两条相交直线垂直.在本题中,我们选取的是平面
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230125-61063.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230127-70496.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230127-81004.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230127-49096.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230127-70496.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230124-79629.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230124-94275.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230124-90030.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230124-83223.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230124-45368.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230124-33984.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230127-62674.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230126-37838.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230124-45368.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230127-50578.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230127-70946.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230128-61666.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230128-93876.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230128-91107.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230126-34579.png)
试题解析:(Ⅰ)依题意,
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230128-90527.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230128-39514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230128-18112.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230128-77575.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230129-90835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230127-62674.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230125-25193.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230124-79629.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230129-72522.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230124-79629.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230127-81004.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230129-57205.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230129-85110.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230127-49096.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230129-72522.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230125-61063.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230125-87310.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230125-61063.png)
(Ⅱ)取
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230127-50578.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230127-70946.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230128-61666.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230129-62553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230130-40429.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230130-30479.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230128-93876.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230126-50094.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230126-37838.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230130-86537.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230130-55623.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230131-54294.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230131-73848.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230131-16686.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230131-18604.png)
解法2:以
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230132-23942.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230132-23942.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230132-44525.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230132-43183.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230132-25467.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230133-19812.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230133-13679.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230133-96472.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230133-58908.jpg)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230133-66354.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230134-47050.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230134-29855.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230134-28020.png)
(Ⅰ)设平面
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230134-40927.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230135-20962.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230135-18548.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230135-70441.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230135-29075.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230136-86124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230136-61277.png)
同理可得平面
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230136-91597.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230136-43330.png)
直接计算知
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230136-46387.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230125-87310.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230125-61063.png)
(Ⅱ)由
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230125-64309.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230137-54150.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230137-73760.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230137-66867.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230137-40688.png)
所以异面直线
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230126-50094.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230126-37838.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230138-29384.png)
(Ⅲ)由(Ⅱ)可知
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230131-54294.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230125-61063.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230138-21162.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230138-14536.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230137-40688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230138-36071.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230139-29766.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230139-28478.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230139-70596.png)
设二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230126-34579.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230139-62950.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230139-62950.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230139-43945.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230140-80408.png)
所以二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230126-34579.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230127-75287.png)
核心考点
试题【如图,四棱柱的底面是平行四边形,且,,,为的中点,平面.(Ⅰ)证明:平面平面;(Ⅱ)若,试求异面直线与所成角的余弦值;(Ⅲ)在(Ⅱ)的条件下,试求二面角的余弦值】;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/20191020/20191020230105-34106.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230106-58701.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230106-16186.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230106-27733.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230106-75546.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230107-30707.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230107-62722.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230107-29587.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230107-53121.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230108-99528.png)
(2)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230108-84385.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230108-88658.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230108-62789.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230048-41799.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230048-63217.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230048-98515.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230048-78775.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230049-31112.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230049-36690.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230049-58658.png)
(Ⅰ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230049-56925.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230050-63406.png)
(Ⅱ)试在棱
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230050-75194.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230050-33575.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230050-14848.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230051-47389.png)
(Ⅲ)在(Ⅱ)的条件下,求
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230051-99452.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230050-63406.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230031-20144.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230031-68910.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230032-52651.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230032-40295.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230032-27338.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230032-63451.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230033-45271.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230033-17258.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230033-61964.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230033-87913.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230033-70150.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230034-74027.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230034-70838.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230034-33457.png)
(Ⅰ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230035-19276.png)
(Ⅱ)求二面角E−AC−D的余弦值
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230017-35965.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230017-41907.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230017-39982.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230017-58187.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230018-67877.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230018-17924.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230018-96541.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230018-18132.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230018-11198.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230019-12198.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230019-89381.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230019-69357.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230019-52223.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230019-91503.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230020-77845.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230020-70333.png)
(Ⅰ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230020-71504.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230020-87841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230021-60685.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230021-33614.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230021-43851.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230022-79939.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230021-33614.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230001-75161.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230002-84680.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230002-84113.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230002-84680.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230002-68946.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230002-29614.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230003-86586.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230003-74451.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230003-52544.png)
(2)求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230003-17555.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230004-69257.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230004-50437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230004-70641.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020230004-69257.png)
最新试题
- 12008年5月是新疆自治区第26个民族团结教育月。新疆阿克苏地区以“畅谈辉煌成就·携手团结奋进”为主题,以“共产党好、社
- 2选词填空。A. their B. gift C. understand D. m
- 3“安能摧眉折腰事权贵,使我不得开心颜”、“孤帆远影碧空尽,唯见长江天际流”、“君不见黄河之水天上来,奔流到海不复回”、“
- 4_____ anyone phone, tell them I"m in conference.[ ]A. Wo
- 5下列地理事物在亚、欧分界线上的是( )A.苏伊士运河B.白令海峡C.巴拿马运河D.土耳其海峡
- 6下图是大型爱国主义专题教育片《新中国外交风云录》(共30集)的封面。根据所学,请你判断属于中国70年代外交成果的是 [
- 7People think it _____ great fun to surf on _____ Internet.[
- 8解不等式>1的解集。
- 9一辆长30m的大型平板车,在匀速通过70m长的大桥时,所用时间是10s,它以同样的速通过另一座桥,用了20s的时间,那么
- 10如图,把边长为3的正三角形绕着它的中心旋转80°后,则新图形与原图形重叠部分的面积为( )A.B.C.D.
热门考点
- 1一个小正方体的六个面,三个面上标以数字0,两个面上标以数学1,一个面上标以数字2(1)甲、乙两人各抛掷一次,谁的点数大谁
- 2如图,△ABC中,∠C=90°,tan∠A=45,D为AC上一点,BC=CD=4,求△ABD的周长.
- 3经过十年的奋起直追,中国网民总数达到2. 85亿,互联网普及率达到36.2%,手机网民达到3. 18亿。微博井喷式发展大
- 4读“珠峰垂直自然带”,完成下列问题。(1)珠峰南北山麓的海拔大约各是多少?各处在哪一热量带?______________
- 5In the worst-affected regions, many areas remain in chaos(混乱
- 6(1)用配方法把二次函数y=x2-4x+3变成y=(x-h)2+k的形成;(2)在直角坐标系中画出y=x2-4x+3的图
- 7下列4幅图中示意马六甲海峡的是( )
- 8下面表格左栏中的内容是2007年3月温家宝总理在《政府工作报告》中提出的2007年国民经济和社会发展的主要目标。请在右栏
- 92009年春夏之际,世界上多个国家和地区出现了甲型H1N1流感。甲型H1N1流感与普通流感一样“可防可治”。甲型H1N1
- 109月27日,航天员_______第一次把中国人的足迹留在了太空。[ ]A、杨利伟 B、翟志刚