题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005712-42519.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005712-73144.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005712-42215.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005713-90887.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005713-99989.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005713-30814.jpg)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005713-62990.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005714-59741.png)
(2)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005714-67079.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005714-91360.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005714-59515.png)
(3)在线段
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005713-99989.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005714-49410.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005714-59095.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005715-42938.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005715-55927.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005715-80798.png)
解析
试题分析:(1)利用三角形的中位线定理证明;(2)证明
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005715-98031.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005715-62161.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005715-58615.png)
试题解析:(1)连结
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005716-34881.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005716-13060.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005716-87366.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005716-75461.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005717-79644.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005716-87366.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005716-34881.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005713-90887.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005713-99989.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005717-80828.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005716-75461.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005717-78331.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005717-46340.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005715-62161.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005718-21955.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005715-62161.png)
所以,
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005717-78331.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005715-62161.png)
(2)因为正方形
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005712-42519.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005712-73144.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005718-66024.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005718-95578.png)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005718-20124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005715-98031.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005715-62161.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005719-98543.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005715-62161.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005715-58615.png)
(3)存在满足条件的
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005715-80798.png)
依题意,以
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005719-68723.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005719-52340.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005719-89431.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005720-68712.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005720-73155.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005720-52422.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005721-28454.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005712-42215.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005721-40235.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005721-43782.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005721-77970.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005722-79645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005722-92877.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005722-20909.png)
易知
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005722-35573.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005723-73676.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005723-18940.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005723-87735.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005723-32292.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005724-43822.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005724-90795.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005724-19658.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005724-19283.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005725-70439.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005725-90487.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005714-59095.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005715-42938.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005725-87615.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005725-16779.png)
故在线段
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005713-99989.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005714-49410.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005714-59095.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005715-42938.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005715-80798.png)
核心考点
试题【如图所示,正方形与矩形所在平面互相垂直,,点为的中点.(1)求证:∥平面;(2)求证:;(3)在线段上是否存在点,使二面角的大小为?若存在,求出的长;若不存在,】;主要考察你对平面的法向量等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005657-74963.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005657-11867.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005657-66519.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005657-77979.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005658-90600.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005658-37206.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005658-97164.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005658-83645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005659-78532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005659-22161.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005659-35675.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005700-42686.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005700-79848.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005700-33476.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005657-11867.png)
(2)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005701-67401.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005701-24641.png)
(3)能否在
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005701-10963.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005701-85336.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005702-61891.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005658-90600.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005701-85336.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005643-75171.jpg)
(1) 证明:BD⊥平面PAC;
(2) 若PA=1,AD=2,求二面角B-PC-A的正切值.
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005619-43354.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005619-71969.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005619-85311.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005620-27031.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005620-55518.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005620-51484.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005620-26134.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005621-91733.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005621-62033.jpg)
(Ⅰ) 求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005621-55522.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005622-79231.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005622-57689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005622-68049.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005605-72418.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005606-14662.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005606-90275.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005606-12006.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005606-69340.png)
(2)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005606-48592.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005552-33029.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005553-88027.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005553-38879.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005553-60063.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005553-50007.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005553-21399.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005553-51541.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005554-60088.png)
(Ⅰ)把向量
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005554-35052.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005554-73226.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005554-82523.png)
(Ⅱ)把向量
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005554-13207.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005554-70470.png)
(Ⅲ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005554-42788.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005554-30900.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005554-95393.png)
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