题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073356-35076.gif)
(Ⅰ)求证:AC⊥BC1
(Ⅱ)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073356-12739.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073356-10386.gif)
(Ⅰ)证明:直三棱柱ABC-A1B1C1,底面三边长AC=3,BC=4,AB=5,
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073356-17510.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073356-39778.gif)
∴ AC⊥BC, …………………2分
又 AC⊥
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073356-95301.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073356-30317.gif)
∴ AC⊥平面BCC1,又
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073356-87430.gif)
∴ AC⊥BC1 ……………………………………5分
(Ⅱ)解法一:取
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073356-54156.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073356-16821.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073357-43311.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073357-14535.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073357-41595.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073357-72347.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073357-71182.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073356-17510.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073357-43311.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073357-40514.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073357-67030.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073357-22544.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073358-34746.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073358-43214.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073358-34746.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073356-17510.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073358-54087.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073358-34746.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073356-87430.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073358-34746.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073358-55216.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073358-36194.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073356-17510.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073357-14535.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073358-85074.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073358-65020.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073358-57150.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073358-54087.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073358-57150.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073358-24715.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073356-17510.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073357-14535.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073358-34799.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073359-35671.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073356-17510.gif)
∴在
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073359-92958.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073358-55216.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073359-54227.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073359-60747.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073359-95697.gif)
∴二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073359-35671.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073359-54614.gif)
解法二:以
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073400-68257.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073400-35476.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073356-17510.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073400-49916.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073400-88574.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073401-22906.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073401-94073.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073401-95396.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073401-56218.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073402-98608.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073402-36991.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073402-28565.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073402-69790.gif)
设平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073403-67506.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073403-85595.gif)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073403-82335.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073403-92253.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073356-12739.gif)
则由
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073404-28810.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073404-36423.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073404-47470.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073404-55004.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073404-21497.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073405-12490.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073405-12155.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073405-36212.gif)
∵二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073359-35671.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073405-37290.gif)
∴二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073359-35671.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073359-54614.gif)
解析
核心考点
试题【(本题满分12分)如图, 在直三棱柱ABC-A1B1C1中,AC=3,BC=4,,AA1=4,点D是AB的中点(Ⅰ)求证:AC⊥BC1(Ⅱ)求二面角的平面角的正】;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/20191022/20191022073347-88461.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073347-53905.png)
①
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073347-64310.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073348-34697.png)
③
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073348-79695.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073348-61686.png)
其中说法正确个数是
A.1 | B.2 | C.3 | D.4 |
EF=
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073340-17585.png)
|
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073341-26071.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073341-21839.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073341-55205.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073341-95218.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073342-36912.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073334-74684.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073331-73946.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073331-41929.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073332-95091.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073332-29687.gif)
|
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073332-57342.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073325-42766.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073325-25391.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073326-11360.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073326-54418.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073326-10199.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073326-78562.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073327-14445.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073327-10066.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073327-94398.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073327-30888.gif)
(Ⅰ)求三棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073327-91245.gif)
(Ⅱ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022073328-19503.gif)
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