题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005243-12086.jpg)
(1).求证:D1E⊥A1D;
(2).在线段AB上是否存在点M,使二面角D1-MC-D的大小为
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005244-88886.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005244-62003.png)
解析
试题分析:本题主要考查线面的位置关系、二面角等基础知识,意在考查考生的空间想象能力推理论证能力.第一问,利用
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005244-45099.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005244-32998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005245-86782.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005245-56314.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005244-45099.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005245-56850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005245-86782.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005244-45099.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005245-56850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005245-86782.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005245-56314.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005245-52326.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005245-39746.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005246-16067.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005246-58302.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005246-78683.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005246-60063.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005247-69570.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005247-39413.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005247-59108.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005247-64421.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005247-33891.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005248-87030.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005248-90776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005248-87933.png)
试题解析:(1)连结
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005244-32998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005245-56314.png)
∵四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005244-45099.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005244-32998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005245-86782.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005245-56314.png)
∵正方形
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005244-45099.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005248-99260.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005248-29641.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005245-56850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005245-86782.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005244-45099.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005244-32998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005249-69468.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005244-45099.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005245-56850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005245-86782.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005245-56314.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005244-32998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005249-28577.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005249-51901.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005245-52326.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005245-39746.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005249-27955.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005250-84299.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005250-50012.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005246-16067.png)
(2)存在满足条件的
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005244-62003.png)
【解法一】假设存在满足条件的点
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005250-18270.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005250-86386.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005246-58302.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005250-38898.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005251-70274.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005246-78683.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005251-31485.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005251-61896.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005246-60063.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005247-69570.png)
9分
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005247-39413.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005247-59108.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005251-57056.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005252-77800.png)
又在
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005247-64421.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005252-18747.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005252-99383.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005252-17546.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005248-90776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005252-24814.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005253-57686.png)
故在线段
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005253-86230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005250-18270.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005247-69570.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005244-88886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005253-57686.png)
【解法二】依题意,以
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005250-86386.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005253-74878.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005253-27257.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005254-25644.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005254-33987.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005254-81678.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005254-49536.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005254-21017.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005255-72454.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005255-37469.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005255-20277.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005255-92096.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005256-96938.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005256-38855.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005256-43997.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005256-24894.png)
易知
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005256-23154.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005257-84010.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005257-33164.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005257-99540.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005257-22908.png)
设平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005257-93439.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005258-31026.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005258-74805.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005258-50495.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005258-98827.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005259-83552.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005259-49879.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005259-16373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005244-88886.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005259-98367.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005259-97565.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005300-92604.png)
又因为
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005300-73245.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005300-24822.png)
故在线段
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005253-86230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005250-18270.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005259-16373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005244-88886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005300-18249.png)
核心考点
试题【如图所示,正方形AA1D1D与矩形ABCD所在平面互相垂直,AB=2AD=2,点E为AB的中点,(1).求证:D1E⊥A1D;(2).在线段AB上是否存在点M,】;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/20191022/20191022005239-70274.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005239-99366.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005239-98662.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005240-48715.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005240-65183.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005232-43922.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005232-73661.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005233-16296.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005233-52424.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005233-10356.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005222-19887.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005222-87828.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005223-99361.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005223-12160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005223-62857.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005223-16044.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005223-93181.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005224-92729.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005204-10255.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005205-63750.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005205-57781.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005205-65952.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005205-82591.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005205-19203.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005206-36576.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005206-31506.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005206-51447.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005206-99341.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005207-89538.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005152-68558.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005152-15059.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005153-65977.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005153-77944.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005153-97824.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005153-52054.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005154-80288.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005154-46211.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005154-39084.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005154-53288.png)
(2)当三棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005154-72991.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022005153-52054.png)
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