题目
题型:不详难度:来源:
B沿棱柱侧面经过棱C C1到点A1的最短路线长为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040931-61238.gif)
点为D.
(1)求三棱柱ABC-A1B1C1的体积;
(2)在平面A1BD内是否存在过点D的直线与平面ABC平行?证明你的判断;
(3)证明:平面A1BD⊥平面A1ABB1.
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040931-49188.jpg)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040931-64669.gif)
(3)证明见解析
解析
设棱柱的棱长为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040931-19356.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040931-19356.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040932-13533.jpg)
∵CD∥AA1 ∴D为CC1的中点,……………………………2分
在Rt△A1AB2中,由勾股定理得
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040932-63270.gif)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040932-58401.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040932-54186.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040933-94064.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040933-10934.gif)
(2)设A1B与AB1的交点为O,连结BB2,OD,则
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040933-93724.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040933-13880.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040933-85640.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040934-84363.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040933-85640.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040934-13940.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040933-85640.gif)
即在平面A1BD内存在过点D的直线与平面ABC平行 ……………………………9分
(3)连结AD,B1D∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040934-13851.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040934-52928.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040935-60567.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040935-58158.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040935-37362.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040935-42393.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040935-73287.gif)
又∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040936-42244.gif)
核心考点
试题【如图,已知三棱柱ABC-A1B1C1的所有棱长都相等,且侧棱垂直于底面,由B沿棱柱侧面经过棱C C1到点A1的最短路线长为,设这条最短路线与CC1的交点为D.(】;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/20191021/20191021040917-50530.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040917-13968.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040917-95334.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040917-60512.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040918-61312.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040918-36811.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040918-62474.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040918-61312.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040918-58713.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040918-10605.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040919-76677.gif)
(1)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040919-42949.gif)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040919-13769.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040919-26982.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040920-71085.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040909-92212.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040909-93679.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040909-32546.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040910-69659.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040910-13033.gif)
A.24 | B.36 | C.44 | D.56 |
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040852-13397.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040853-72249.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040853-39826.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040853-72249.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040853-31056.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040853-76492.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040854-13598.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040854-45053.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040854-77119.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040854-64607.gif)
(I)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040854-21462.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040855-27481.gif)
(II)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040855-61069.gif)
(III)求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040855-66491.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040855-60724.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040856-98745.jpg)
已知正三棱柱
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040841-44265.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040842-44728.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040842-81575.gif)
(Ⅰ)试证明
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040842-55327.gif)
(Ⅱ)若直线AD与侧面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040842-97085.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040843-94055.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040843-34837.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040843-10126.jpg)
最新试题
- 1函数f(x)的定义域为[0,1],且满足以下三个条件:①f(0)=0;②f(x3)=12f(x);③f(1-x)=1-f
- 2Please _____ the milk into the blender. [ ]A. p
- 3The humans are destroying nature day by day, _____ of course
- 4灰锡(以粉末状存在)和白锡是锡的两种同素异形体。已知:①Sn(白,s)+2HCl(aq)===SnCl2(aq)+H2(
- 5某同学想描绘某一热敏电阻的伏安特性曲线,实验室提供下列器材:A.电压表V(量程为0-5V,内阻约5k)B.电流表A1(量
- 6如图,三个天平的托盘中形状相同的物体质量相等.图(1)、图(2)所示的两个天平处于平衡状态,要使第三个天平也保持平衡,则
- 7We should carefully _________ the case, and we cannot declar
- 8下列各组离子在常温下一定能大量共存的是A.pH=0的无色溶液中:Cl-、Na+、SO42-、Fe2+B.在c(H+)=1
- 9如图所示,为由基本门电路组成的四个电路,其中能使小灯泡发光的是( )A.B.C.D.
- 10________ I"ll be in ten more years.[ ]A. What do you thi
热门考点
- 1下列说法中正确的有________①刻画一组数据集中趋势的统计量有极差、方差、标准差等;刻画一组数据离散程度统计量有平均
- 2点P(-2,3)关于y轴对称点的坐标是 [ ]A.(-2,3) B.(2,-3)C.(2,3) D(-2,-3)
- 3根据句义,用所给词的适当形式填空,每空填一个词。 1. What"s Li Ming doing? He ____
- 4如图,抛物线的对称轴是直线,且经过点(3,0),则的值为( )A.0B.-1C. 1D. 2
- 5一辆赛车在半径为50m的水平圆形赛道参加比赛,已知该赛车匀速率跑完最后一圈所用时间为15s。则该赛车完成这一圈的角速度大
- 6【题文】 朱光潜先生《谈美》一书中介绍过近代一些有趣的美学实验。如瑞士心理学家布洛关于颜色的重量实验:把两个面积、角度均
- 7命题“如果a,b都是奇数,则ab必为奇数”的逆否命题是( )A.如果ab是奇数,则a,b都是奇数B.如果ab不是奇数,
- 8如图所示,竖直放置的长直导线通以恒定电流,有一矩形线圈与导线在同一平面上,在下列状况中线框中不能产生感应电流的是A.导线
- 9如图,把1,3,6,10,15,…这些数叫做三角形数,这是因为这些数目的点可以排成一个正三角形,则第七个三角形数是A.2
- 10《联合国宪章》规定的联合国的宗旨,简单地说就是A.调节国际争端,消除国家间矛盾B.维护国际和平与安全,促进国际合作与发展