题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022411-45845.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022411-54448.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022411-29304.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022411-34865.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022412-66119.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022412-82771.jpg)
(1)求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022412-18081.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022413-36327.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022413-62985.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022412-18081.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022413-31166.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022414-98509.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022414-84941.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022414-69698.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022414-82783.png)
(3)在(2)的条件下,求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022414-16737.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022415-35227.png)
解析
试题分析:(1)通过证明平行四边形分别证明
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022415-73460.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022415-26859.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022415-20166.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022413-36327.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022416-91013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022413-36327.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022416-36209.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022413-36327.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022416-12261.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022416-51415.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022416-76788.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022417-45996.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022416-51415.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022417-95299.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022414-69698.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022414-82783.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022411-29304.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022417-34630.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022417-62995.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022418-16007.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022418-80077.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022418-88395.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022418-51852.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022414-69698.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022414-82783.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022419-34526.png)
试题解析:(1)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022419-17699.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022419-76718.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022420-90645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022416-51415.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022420-90471.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022420-84799.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022413-36327.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022420-26973.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022421-53456.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022413-36327.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022421-15966.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022413-36327.png)
同理可得
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022416-91013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022413-36327.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022421-25482.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022420-90645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022416-36209.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022413-36327.png)
(2)证法1:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022421-38398.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022412-18081.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022422-75664.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022416-51415.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022420-90645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022416-51415.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022422-98266.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022412-18081.png)
平面
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022416-51415.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022422-45136.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022422-10892.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022423-71727.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022423-61996.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022414-98509.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022414-84941.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022423-21058.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022423-62740.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022424-88205.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022416-51415.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022424-23319.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022424-14156.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022424-64993.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022425-59316.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022425-99455.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022416-51415.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022425-89624.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022425-22311.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022426-15463.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022414-82783.png)
证法2:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022426-69701.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022414-98509.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022414-84941.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022426-10706.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022426-57316.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022421-38398.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022427-94228.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022427-18406.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022427-34035.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022427-94228.png)
以点
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022411-29304.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022417-34630.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022417-62995.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022418-16007.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022418-80077.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022418-88395.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022418-51852.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022427-84874.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022427-98878.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022428-18835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022428-11847.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022428-52334.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022428-24801.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022429-27329.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022429-80733.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022429-90466.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022429-25596.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022430-25869.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022430-91358.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022430-87323.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022430-77865.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022426-15463.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022431-12416.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022431-50064.png)
(3)由(2)得
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022431-66071.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022431-25736.png)
设平面
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022432-54220.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022432-31065.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022432-75053.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022432-53676.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022433-20689.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022433-87364.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022433-59140.png)
由(2)知
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022433-80391.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022431-12416.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022434-88071.png)
即二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022414-16737.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022434-16456.png)
(其它解法请参照给分)
核心考点
试题【如图,已知、、为不在同一直线上的三点,且,.(1)求证:平面//平面;(2)若平面,且,,,求证:平面;(3)在(2)的条件下,求二面角的余弦值.】;主要考察你对向量与空间位置关系等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022352-38990.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022352-72688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022352-54580.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022353-24602.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022353-63547.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022353-25035.jpg)
(1)求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022353-56539.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022353-91512.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022354-65235.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022353-56539.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022354-80049.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022354-50263.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022355-55751.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022355-99183.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022400-76783.png)
(3)在(2)的条件下,设点
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022400-69645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022401-59445.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022401-44605.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022401-74165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022336-65571.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022336-82804.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022336-37613.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022337-96033.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022337-82193.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022337-42333.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022337-70290.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022337-99985.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022337-74480.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022337-19435.png)
(2)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022337-57309.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022323-59779.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022323-53432.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022323-81441.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022323-38617.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022324-52114.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022324-19180.png)
(2)若平面
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022324-96600.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022324-56657.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022324-90598.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022325-98860.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022255-62651.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022255-83075.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022255-62651.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022256-72291.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022256-12419.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022256-83661.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022256-27347.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022256-94162.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022256-76582.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022256-30742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022256-60788.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022257-48292.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022257-34360.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022257-51642.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022257-67765.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022257-58843.png)
(2)求平面
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022257-86614.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022257-63852.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022241-94312.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022241-14534.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022241-55314.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022241-90347.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022242-64336.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022242-94818.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022242-13969.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022242-22616.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022243-18248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022243-56877.png)
(Ⅰ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022243-21432.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022243-86894.png)
(Ⅱ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022244-90467.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022244-31979.png)
(Ⅲ)试问在线段
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022244-75110.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022244-49365.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022242-94818.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022242-13969.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022244-49365.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022243-86894.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106022244-49365.png)
最新试题
- 1有三只相同的杯子里盛有体积不等的水,将质量相等的实心铁块、铝块、铜块分别浸没在这三只杯子的水中,水未溢出,通过比较他发现
- 2【题文】依次填入下列各句横线处的词语,最恰当的一组是
- 3信息匹配(共5小题;每小题2分,满分10分)阅读下列应用文及相关信息,并按照要求匹配信息。(E填涂AB,F填涂AC)A.
- 4雅典奴隶制民主政治发展到全盛时期是在梭伦时期。
- 5工业上可用食盐和石灰石为主要原料,经不同的方法生产纯碱。请回答下列问题:(1)路布兰法是以食盐、石灰石、浓硫酸、焦炭为原
- 6While studying, fix your mind on what is really important, o
- 717. Children brought up in cities are often full of _______
- 8海南是我国最大的经济特区和热带岛屿。2010年国务院提出建立海南国际旅游岛。图为其规划示意图,读图完成题。小题1:海南铁
- 9沿海地区同沙漠地区相比,冬暖夏凉,昼夜温差小,这是因为 [ ]A.水的密度比沙石的密度小 B.水的比热容大于沙石
- 10下列各溶液中的离子可能大量共存的是A.某无色透明溶液:Na+、CO32-、K+、S2-、SO32-B.由水电离的c(OH
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- 1给你一只手表,利用你们家用的电能表测出一个功率未知的电冰箱一个月约消耗的电功大约是多少?已知家中电能表铭牌上标有3000
- 2(1)解方程:x2-2x-3=0;(2)计算:(212-313)×6.
- 3Ⅰ通过学习化学,我们认识了很多化学物质的性质和用途.请你选择适当的物质在以下的选项中填空(填序号).①不锈钢 ②金刚
- 4I hear ________ students went to the hall to have the concer
- 5玄奘西游是_________初年。
- 6美国加州Miramal海军航空站安装了一台250kW的MCFC型燃料电池,该电池可同时供应电和水蒸气,其工作温度为600
- 7计算:(1)-4.2+2.7+4.2-3.7(2)(23-112-415)×60(3)[-14-(1-0.5×13)]×
- 8如图,在直三棱柱ABC-A1B1C1,AC⊥BC,AC=BC=BB1,点D是BC的中点.(I) 求证:A1C∥平面AB1
- 9已知,点列部分图象 如图所示,则实数的值为
- 10复数(i是虚数单位)的实部是( ).A.B.-C.-iD.-