题目
题型:不详难度:来源:
已知斜三棱柱
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120311-52633.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120312-77692.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120312-24483.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120312-71734.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120312-95537.gif)
为
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120312-66534.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120312-20470.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120312-30389.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120312-26629.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120313-31781.gif)
(I)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120313-64822.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120313-99311.gif)
(II)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120313-28400.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120313-47210.jpg)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120313-78597.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120314-43126.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120314-87103.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120314-78855.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120312-95537.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120314-13802.jpg)
以
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120314-63669.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120314-21339.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120315-93058.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120315-15050.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120315-92077.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120315-40965.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120315-97789.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120316-90373.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120316-14885.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120316-46375.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120316-89178.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120317-37373.gif)
知
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120317-89008.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120313-31781.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120313-64822.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120313-99311.gif)
(II)由
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120317-66870.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120318-51856.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120318-60743.gif)
设平面
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120318-62407.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120318-18391.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120318-71213.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120319-82796.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120319-35020.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120319-92995.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120319-47619.gif)
再设平面
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120319-34331.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120320-21395.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120320-84829.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120320-12929.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120320-54521.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120319-92995.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120321-71932.gif)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120321-81785.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120321-58324.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120313-28400.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120321-58324.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120322-35602.jpg)
法二: (I)如图,
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120313-78597.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120314-43126.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120314-78855.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120312-95537.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120322-93125.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120312-77692.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120322-51382.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120322-40652.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120313-31781.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120313-64822.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120313-99311.gif)
(II)由(I)知
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120323-85202.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120323-82348.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120323-38442.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120323-75575.gif)
作
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120324-87234.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120324-74817.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120324-64753.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120324-24607.gif)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120324-63825.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120325-31624.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120325-66464.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120325-24569.gif)
故二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120313-28400.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120321-58324.gif)
解析
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120247-79827.gif)
如图,在四棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120248-58234.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120248-45433.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120248-31492.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120248-45433.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120248-74085.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120248-93406.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120249-45912.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120249-30687.gif)
(Ⅰ)证明
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120249-52420.gif)
(Ⅱ)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120249-69755.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120250-13416.gif)
如图,四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120236-31513.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120236-74772.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120237-24140.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120237-40373.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120237-24140.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120237-40373.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120237-35373.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120237-10898.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120237-18354.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120237-80022.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120237-38255.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120237-80022.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120237-82024.jpg)
(Ⅰ)求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120238-66266.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120238-22995.gif)
(Ⅱ)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120238-31060.gif)
(本小题共l2分)
如图,在直三棱柱AB
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120226-36547.gif)
P是AD的延长线与A1C1的延长线的交点,且PB1∥平面BD
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120227-62277.gif)
(I)求证:CD=C1D:
(II)求二面角A-A1D-B的平面角的余弦值;
(Ⅲ)求点C到平面B1DP的距离.
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120227-90972.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120222-48309.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120222-83666.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120222-55963.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120216-95464.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105120216-42886.gif)
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