题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044959-89206.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044959-19118.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044959-37961.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045000-33747.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044959-19118.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045000-99507.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045000-43202.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045000-41593.gif)
(Ⅰ) 求证:四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045000-18529.gif)
(Ⅱ) 求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045001-52803.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045001-30041.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045001-76906.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045001-56678.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045001-93580.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045001-31105.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045002-87176.gif)
因为四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044959-19118.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045002-83265.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045002-67368.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045002-58133.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045003-70450.gif)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045003-84987.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045003-54691.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045003-77368.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045003-77368.gif)
(Ⅱ) 连接OE,因为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045003-67879.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045004-98476.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045004-28833.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045004-82332.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045004-53480.gif)
E─
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045000-99507.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044959-19118.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045004-71884.gif)
又E是
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045000-43202.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045005-37193.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045005-32828.gif)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045005-25604.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045005-26399.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045005-41946.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045005-53565.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045006-50147.gif)
所以在△
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045006-41453.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045006-86768.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045001-56678.gif)
(Ⅲ) 设点D到平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045006-81740.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045006-49983.gif)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045006-39571.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045007-11781.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045007-26889.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045007-86250.gif)
解法二:(Ⅰ) 连结AC、BD相交于O,连结
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045007-95361.gif)
由已知,有AC⊥BD,
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045007-95361.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045008-47995.gif)
且以下各点的坐标分别为:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045008-73427.gif)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045008-78627.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045008-15363.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045008-31560.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045009-49078.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045009-90350.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045009-76252.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045009-26446.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045008-15363.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045000-18529.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045009-58230.gif)
(Ⅱ) 设
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045010-74729.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045010-45280.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045010-40563.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045010-28209.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045010-17165.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045011-67756.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045011-51038.gif)
则由
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045011-32769.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045011-84156.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045011-82985.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045011-76334.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045012-34303.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045012-24438.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045012-63102.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045012-16044.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045012-64422.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045013-92674.gif)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045013-17825.gif)
∴ 二面角E─BD─C的大小为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045001-56678.gif)
(Ⅲ) 设
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045013-81311.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045013-78925.gif)
则由
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045013-13187.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045014-29306.gif)
∴ 可取
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045014-52352.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045014-81815.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045014-34669.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045013-78925.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045014-73913.gif)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045014-30893.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045015-25020.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021045015-50165.gif)
核心考点
试题【(满分14分)在斜四棱柱中,已知底面是边长为4的菱形,,且点在面上的射影是底面对角线与AC的交点O,设点E是的中点,.(Ⅰ) 求证:四边形是矩形;(Ⅱ) 求二面】;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
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044953-96906.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044953-96395.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044953-14455.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044954-38084.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044954-92856.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044954-15280.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044953-96906.gif)
(1) 求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044954-68816.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044954-56201.gif)
(2) 求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044955-65716.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044955-28123.gif)
(3) 若
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044955-20318.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044955-36404.gif)
体积.
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044947-16701.jpg)
角BDA=60°, 角BCD=135°求BC的长.
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044941-67656.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044941-55463.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044935-36851.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044935-42920.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044935-36851.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044936-18617.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044926-73538.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044927-54199.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044927-40498.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044927-89685.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044927-46262.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044927-70956.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044928-87184.gif)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044928-27619.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044927-40498.gif)
(2)求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044928-96557.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044928-16917.gif)
(3)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044929-82891.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044928-96557.gif)
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