题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002711-66329.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002711-10589.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002712-42024.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002712-95143.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002712-98976.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002712-11728.png)
(Ⅰ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002713-99069.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002713-94019.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002713-84930.png)
(Ⅲ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002713-94019.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002713-50407.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002714-18160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002714-50237.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002714-90412.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002714-18160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002714-16665.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002715-71483.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002712-42024.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002712-95143.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002715-52872.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002715-29732.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002715-53250.png)
又∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002712-98976.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002716-67360.png)
∴斜线
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002716-81465.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002711-10589.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002716-93379.png)
∴由三垂线定理,得
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002716-74312.png)
故,
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002717-90233.png)
(Ⅱ)以
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002717-94873.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002717-13240.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002717-91032.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002718-60382.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002718-54593.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002718-33088.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002718-30921.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002718-31261.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002719-89418.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002719-31511.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002719-63286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002719-84561.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002719-30487.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002719-89418.png)
同理可求:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002720-65014.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002720-83631.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002720-24507.png)
故,二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002713-84930.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002720-49945.png)
(Ⅲ)显然
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002720-34038.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002721-32667.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002721-90182.png)
因
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002721-24450.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002722-39332.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002722-61665.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002722-67323.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002722-59065.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002723-14916.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002723-34684.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002723-14916.png)
由题意,得
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002723-40530.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002723-98295.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002724-98997.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002724-30764.png)
故,当点
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002714-18160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002713-50407.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002724-93168.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002714-50237.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002724-12237.png)
解析
核心考点
试题【如图,四棱锥中,底面是平行四边形,底面(Ⅰ)求证:;(Ⅱ)若,求二面角的余弦值;(Ⅲ)当时,在线段上是否存在一点使二面角为,若存在,试确定点的位置;若不存在,请】;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/20191021/20191021002703-48962.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002703-40868.png)
① 若
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002703-90329.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002703-65677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002704-72773.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002704-39150.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002703-48962.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002704-28423.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002704-22595.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002704-72773.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002704-72773.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002704-79218.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002705-47861.png)
A.2 | B.![]() | C.3 | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002644-79972.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002633-15975.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002633-12986.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002633-32871.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002633-70926.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002634-23401.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002634-74703.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002634-82900.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002634-41952.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002634-21674.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002635-51250.png)
(1) 证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002635-37094.png)
(2) 证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002635-70586.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002635-17071.png)
(3) 求四棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002633-15975.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002622-50785.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002623-10903.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002623-17347.png)
(3
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002623-60271.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021002624-33765.png)
其中正确命题的个数是
A.0 | B.1 | C.2 | D.3 |
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