题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071232-13310.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071232-53398.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071232-61549.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071232-10477.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071233-84916.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071233-79849.png)
(I)当
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071233-67126.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071233-64634.png)
(II)设二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071233-65926.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071233-55400.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071234-11741.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071234-94818.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071234-63643.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071235-90488.png)
(I)如图1,连结NF、
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071235-45389.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071235-24796.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071235-84736.png)
又底面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071235-84552.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071235-84736.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071236-87384.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071236-49558.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071235-84736.png)
∴NF为EF在侧面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071235-84736.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071236-28595.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071237-48427.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071237-34087.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071235-45389.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071237-81362.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071237-13848.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071237-27551.png)
(II)如图2,连结AF,过N作
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071238-95069.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071236-49558.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071235-84736.png)
根据三垂线定理得
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071238-35601.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071238-97367.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071238-79889.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071239-45947.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071236-28595.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071239-10678.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071239-33288.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071239-97496.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071239-11155.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071240-18204.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071240-77345.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071234-11741.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071240-68282.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071240-72839.png)
解法二:(I)建立如图3所示的空间直角坐标系,则由已知可得
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071241-43272.png)
于是
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071241-23683.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071241-74580.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071237-27551.png)
(II)设
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071241-38090.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071241-77327.png)
则由(I)得
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071242-65069.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071242-73479.png)
于是由
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071242-92123.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071242-49805.png)
取
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071243-58032.png)
又由直三棱柱的性质可取侧面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071235-45389.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071243-79508.png)
于是由
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071233-55400.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071243-89364.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071243-76627.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071244-27935.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071244-23451.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071244-57989.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071244-31784.png)
故当
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071244-41003.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071240-72839.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071234-11741.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071245-53059.png)
解析
核心考点
试题【(本小题满分12分)如图,已知正三棱柱的各棱长都是4, 是的中点,动点在侧棱上,且不与点重合.(I)当时,求证:;(II)设二面角的大小为,求的最小值.】;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/20191022/20191022071226-93691.png)
(1)若侧棱长为
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071227-77375.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071227-46266.png)
(2)若AB1与BC1成
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071227-64294.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071227-39270.png)
(1)当E为AB的中点时,求点E到平面ACD1的距离;
(2)AE等于何值时,二面角D1-EC-D的大小为
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071217-40789.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071217-99706.png)
如图,已知
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071211-52002.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071211-27366.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071212-42668.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071212-54901.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071212-40947.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071211-52002.png)
(1) 证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071212-60985.png)
(2) 若
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071213-94161.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071213-56064.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071213-44607.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071213-52055.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071214-54674.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071214-10630.png)
如图,已知
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071200-69263.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071200-11349.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071201-48359.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071201-91580.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071201-50289.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071201-50255.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071201-95746.png)
(1)求异面直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071201-42570.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071201-98561.png)
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071202-42884.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071202-74072.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071153-27323.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071153-28608.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071153-28608.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022071153-95546.png)
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