题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033802-94255.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033802-98790.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033802-67464.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033802-95992.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033803-63308.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033803-68645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033803-69427.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033803-99885.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033803-82263.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033804-77760.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033804-19776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033804-29143.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033804-43271.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033804-64298.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033805-44239.png)
(2)在线段
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033805-61378.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033805-95692.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033805-55355.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033805-56904.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033806-23519.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033806-23677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033806-37503.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033806-47979.png)
解析
试题分析:(1) 由
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033803-68645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033803-69427.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033802-94255.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033807-91161.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033807-91161.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033804-19776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033804-64298.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033805-44239.png)
(2)由于平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033807-63781.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033807-56060.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033807-19003.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033808-30603.png)
(1) 因为等边△
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033802-94255.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033803-68645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033803-69427.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033808-88949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033808-89778.png)
在△
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033803-99885.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033808-23727.png)
由余弦定理得
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033808-83205.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033809-88568.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033807-91161.png)
折叠后有
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033809-81192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033809-79198.png)
因为二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033804-19776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033804-77760.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033809-51876.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033805-44239.png)
又平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033804-77760.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033810-49838.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033805-44239.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033810-48625.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033810-51761.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033804-77760.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033809-81192.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033804-64298.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033805-44239.png)
(2)由(1)的证明,可知
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033810-32101.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033804-64298.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033805-44239.png)
以
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033802-98790.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033811-26386.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033803-82263.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033811-61537.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033811-51245.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033811-59657.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033811-25835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033812-85484.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033812-21036.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033812-21528.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033812-40840.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033813-67940.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033813-35047.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033813-54517.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033813-95443.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033813-73027.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033814-45679.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033814-59225.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033814-29087.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033805-56904.png)
所以平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033805-56904.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033814-54682.png)
因为直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033805-55355.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033805-56904.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033815-79829.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033815-18037.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033815-44461.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033815-93556.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033815-91242.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033816-33029.png)
所以在线段
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033805-61378.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033805-95692.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033805-55355.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033805-56904.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033815-79829.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033816-74749.png)
核心考点
试题【等边三角形的边长为3,点、分别是边、上的点,且满足(如图1).将△沿折起到△的位置,使二面角成直二面角,连结、 (如图2).(1)求证:平面;(2)在线段上是否】;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/20191022/20191022033751-23305.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033751-85084.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033751-41305.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033752-18427.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033752-99034.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033752-38144.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033752-32350.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033752-30694.png)
(2)求点
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033752-41059.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033753-60566.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033744-34298.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033731-77169.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033731-66104.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033731-69902.png)
(l)求证:平面ADG
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033732-65175.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033732-78831.png)
(2)判断
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033732-47809.png)
(3)若G是
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033731-69902.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033732-64723.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033725-93429.jpg)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033719-55738.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033719-78538.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033719-24300.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033719-15243.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033719-57249.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033720-83720.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033720-22069.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033720-46190.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022033720-41077.png)
A.0条 | B.1条 | C.2条 | D.无数条 |
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