题目
题型:不详难度:来源:
如图,在多面体ABCDEF中,四边形ABCD是正方形,AB=2EF=2,EF∥AB,EF⊥FB,∠BFC=90°,BF=FC.
(1)求证:平面ABFE⊥平面DCFE;
(2)求四面体B—DEF的体积.
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021955-68800.jpg)
答案
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021955-95995.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021955-86154.gif)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021956-11288.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021956-11946.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021956-15483.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021956-19057.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021957-92181.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021956-19057.gif)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021957-13795.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021957-50124.gif)
所以,面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021957-22247.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021956-19057.gif)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021958-25140.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021958-89732.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021958-57260.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021958-54736.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021958-86347.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021959-49324.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021959-68449.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021959-45966.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021959-26921.gif)
所以:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022000-70103.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021959-26921.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022000-19103.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021959-26921.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022000-53115.gif)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022000-83525.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022000-31000.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022001-12415.gif)
由(1)得:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022001-95167.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021956-19057.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022001-49065.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022001-79312.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022002-80031.gif)
所以:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021022002-83928.gif)
核心考点
试题【(本小题10分)如图,在多面体ABCDEF中,四边形ABCD是正方形,AB=2EF=2,EF∥AB,EF⊥FB,∠BFC=90°,BF=FC.(1)求证:平面A】;主要考察你对空间几何体的结构特征等知识点的理解。[详细]
举一反三
如图,三棱锥P-ABC中,PA⊥底面ABC,AB⊥BC,DE垂直平分PC,且分别交AC、PC于D、E两点,又PB=BC,PA="A" B.
(Ⅰ)求证:PC⊥平面BDE;
(Ⅱ)若点Q是线段PA上任一点,求证:BD⊥DQ;
(Ⅲ)求线段PA上点Q的位置,使得PC//平面BDQ.
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021951-62634.jpg)
如图,在长方体
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021940-62568.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021940-73049.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021940-61406.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021940-87877.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021941-44216.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021941-30991.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021941-30392.gif)
(1)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021941-13942.gif)
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021941-95054.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021942-91753.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021942-26730.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021935-10297.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021935-87552.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021935-88437.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021936-75937.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021935-87552.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021936-79160.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021936-68444.gif)
A.0条 | B.1条 | C.2条 | D.无数条 |
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021936-25959.jpg)
①矩形 ②不是矩形的平行四边形
③有三个面为等腰直角三角形,另一个面为等边三角形的四面体
④每个面都是等边三角形的四面体
⑤每个面都是直角三角形的四面体
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021912-23249.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021912-36348.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021912-88950.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021913-94024.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021913-74085.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021913-31014.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021913-29624.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021913-10388.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021913-57666.gif)
(1)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021914-83052.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021914-59514.gif)
(2)求证:直线
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021914-54829.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021914-69399.gif)
(3)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021914-83052.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021914-69399.gif)
|
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021021915-79973.jpg)
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