解答题-问答题 适中0.65 引用1 组卷2799
如图,四棱柱
中,![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/596f01c22a6b4791a2ec63bd661fd429.png)
底面
.四边形
为梯形,
,且
.过
三点的平面记为
,
与
的交点为
.
(1)证明:
为
的中点;
(2)求此四棱柱被平面
所分成上下两部分的体积之比;
(3)若![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/596f01c22a6b4791a2ec63bd661fd429.png)
,
,梯形
的面积为6,求平面
与底面
所成二面角大小.
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/9dfed7d9-ea66-4a82-b56c-9c0ba6638f06.png?resizew=191)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/2fc9ffddd0dd414bb43f277be481882c.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/596f01c22a6b4791a2ec63bd661fd429.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/8cadd2a06907476387af1fab080df0d7.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/260bdd891a01497cb1d5186c01a71651.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/260bdd891a01497cb1d5186c01a71651.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/450b8c92f03241108169cf1af53f4089.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/3add4f59a61140d398a6e8961ed10143.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/c39a275a980c48258e0a9f63850249da.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/04bb3358044143c0a7917a9aba6f5516.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/ad148f0a1a884d7fa7a86cdff63c5822.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/04bb3358044143c0a7917a9aba6f5516.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/613a5ceca8174a10b921e31320d10024.png)
(1)证明:
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/613a5ceca8174a10b921e31320d10024.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/ad148f0a1a884d7fa7a86cdff63c5822.png)
(2)求此四棱柱被平面
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/04bb3358044143c0a7917a9aba6f5516.png)
(3)若
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/596f01c22a6b4791a2ec63bd661fd429.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/cdfb0865f83a4b318854af80e2164293.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/e2a8ab04577541d9aa1dc7c2bcb8d83a.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/260bdd891a01497cb1d5186c01a71651.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/04bb3358044143c0a7917a9aba6f5516.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/260bdd891a01497cb1d5186c01a71651.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571782443687936/1571782449627136/STEM/9dfed7d9-ea66-4a82-b56c-9c0ba6638f06.png?resizew=191)
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