题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043507-96400.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043507-33637.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043507-95041.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043507-55124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043507-37527.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043508-41064.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043508-30654.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043508-29306.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043508-69770.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043508-44218.png)
(2)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043508-85979.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043509-92612.png)
(3)求三棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043509-38364.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043509-24550.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043509-12007.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043510-68322.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043507-55124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043510-25607.png)
(2)利用中位线性质在
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043510-37784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043510-34250.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043510-55559.png)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043511-66804.png)
解析
试题分析:解:(1)证明 取
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043511-89261.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043511-97703.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043511-23607.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043511-11205.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043512-30637.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043512-63577.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043512-37281.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043512-98318.png)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043512-53981.png)
则 在等腰三角形
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043509-12007.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043510-68322.png)
又 在
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043513-35855.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043513-94719.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043513-77618.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043513-30897.png)
因
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043507-55124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043510-25607.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043513-49843.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043510-25607.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043507-55124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043514-15146.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043514-61962.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043514-70498.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043514-34452.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043514-31732.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043515-14716.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043515-20432.png)
由①②知
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043515-24344.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043515-43081.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043515-24344.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043515-34982.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043516-26352.png)
(2)(法一)取
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043516-11404.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043516-50589.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043516-54136.png)
则 在
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043510-37784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043510-34250.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043510-55559.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043516-35654.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043509-92612.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043517-96148.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043509-92612.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043510-34250.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043509-92612.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043517-20940.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043517-24916.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043517-93852.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043517-34548.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043512-63577.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043518-26121.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043518-24489.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043518-88125.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043509-92612.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043518-53403.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043509-92612.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043518-26121.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043509-92612.png)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043519-22808.png)
所以 面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043519-42107.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043509-92612.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043519-79259.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043519-42107.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043519-17527.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043509-92612.png)
(法二)延长
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043519-19726.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043520-10156.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043520-57371.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043520-24872.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043520-62118.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043521-27869.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043514-15146.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043521-49325.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043521-83851.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043521-32586.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043519-17527.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043520-57371.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043521-59757.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043509-92612.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043522-98195.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043509-92612.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043519-17527.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043509-92612.png)
(3)由(1)(2)知
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043512-98318.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043522-65668.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043522-84739.png)
因
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043514-34452.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043514-31732.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043513-77618.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043513-30897.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043522-24547.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043514-31732.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043511-66804.png)
点评:主要是考查了空间中线面的位置关系的判定以及体积的求解,属于中档题。
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043431-13162.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043432-59905.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043432-19980.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043432-90634.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043432-26297.png)
(1)若AE=2,求证:AC∥平面BDE;
(2)若二面角A—DE—B为60°.求AE的长。
A.垂直和平行 | B.均为平行 | C.均为垂直 | D.不确定 |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043423-59571.jpg)
A.是45° | B.是60° |
C.是90° | D.随P点的移动而变化 |
①x、y、z均为直线;②x、y是直线,z是平面;③z是直线,x、y是平面;④x、y、z均为平面,其中使“x⊥z且y⊥z⇒x∥y”为真命题的是 ( )
A.③④ | B.①③ |
C.②③ | D.①② |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043405-10564.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043405-79869.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043405-74387.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043406-96149.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043406-20268.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043406-59025.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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