题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120912-64355.png)
(1)试判断折叠后直线AB与平面DEF的位置关系,并说明理由;
(2)若棱锥E-DFC的体积为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120912-87005.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120912-64355.png)
(3)在线段AC上是否存在一点P,使BP⊥DF?如果存在,求出
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120912-30827.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120912-40914.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120913-70487.png)
解析
试题分析:(1)由于E、F分别是AC和BC边的中点,所以在翻折后的三角形ABC中,
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120913-99038.png)
(2)由棱锥E-DFC的体积为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120912-87005.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120913-94181.png)
(3)在线段AC上是否存在一点P,使BP⊥DF,即转化为直线与平面垂直的问题,假设存在点P作
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120913-52105.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120913-92860.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120914-20249.png)
(1)AB//平面DEF,
如图.在△ABC中,∵E,F分别是AC,BC的中点,故EF//AB,
又AB
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120914-78284.png)
(2)∵AD⊥CD,BD⊥CD, 将△ABC沿CD翻折成直二面角A-DC-B
∴AD⊥BD,AD⊥平面BCD,取CD中点M,则EM//AD,∴EM⊥平面BCD,且EM=a/2
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120914-27177.png)
(3)存在满足条件的点P.
做法:因为三角形BDF为正三角形,过B做BK⊥DF,延长BK交DC于K,过K做KP//DA,交AC于P.则点P即为所求.
证明:∵AD⊥平面BCD , KP//DA,∴PK⊥平面BCD,PK⊥DF,又 BK⊥DF,PK∩BK=K,∴DF⊥平面PKB,DF⊥PB.又∠DBK=∠KBC=∠BCK=30°,∴DK=KF=KC/2.
故AP:OC=1:2,AP:AC=1:3 12分
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120903-15262.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120903-32048.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120903-18263.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120905-91445.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120858-94958.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120858-30686.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120858-90361.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120858-35656.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120858-54445.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120858-76730.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120858-21885.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120858-87191.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120859-63580.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120841-31103.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120841-78960.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120841-34662.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120841-93704.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120841-26260.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120841-25689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120841-77366.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120842-24707.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120842-50353.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120842-33670.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120842-44249.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120842-94934.png)
(2)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120843-96048.png)
(3)求三棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120843-96705.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120843-59171.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120830-78476.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120831-95972.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120831-53216.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120831-95972.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120831-86697.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120831-56900.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120831-85955.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120831-93003.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120831-98254.png)
(1)作出这个几何体的三视图(不要求写作法).
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120831-87272.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120831-37396.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120831-67881.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120831-93408.png)
(3) 求三棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120832-57216.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120832-50380.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120824-94300.png)
最新试题
- 1It’s said that there are plenty of hotels here .There
- 2关于电场和电场线的提出,以下说法正确的是A.库仑提出了电场的概念B.法拉第提出了电场的概念C.库仑提出用电场线描述电场D
- 3细菌和真菌在生物圈的物质循环中起着极为重要的作用,如图甲所示;这一原理也被用于解决生活污水造成的水污染问题.城市居民生活
- 4对下边漫画理解正确的是[ ]A.共同富裕是同时、同等程度的富裕 B.中国共产党始终代表中国最广大人民的根本利益
- 5实验室一瓶放置已久的烧碱,因与空气中的CO2反应生成Na2CO3而变质.为测定该瓶烧碱中NaOH含量,某同学取烧碱样品5
- 6如图,两圆相交于A、B两点,小圆经过大圆的圆心O,点C,D分别在两圆上,若∠ADB=100°,则∠ACB的度数为____
- 7阅读下面的的文言文,完成后面各题。稼 轩 记治之北可里所,故有旷土存,三面傅城,前枕澄湖如宝带,其从千有二百三十尺,其衡
- 8"He who can have patience can have what he wants," said Benj
- 9(本小题满分4分)若某几何体的三视图(单位:)如图所示,则此几何体的体积是 .
- 10一定质量理想气体的状态经历了如图所示的、、、四个过程,其中的延长线通过原点,垂直于..且与水平轴平行,与平行,则气体体积
热门考点
- 1如图所示,某同学用一个闭合线圈套入蹄形磁铁,由1位置经2位置到3位置,最后从下方S极拉出,则在这一过程中,线圈中的感应电
- 2把一副常用的三角形如图所示拼在一起,那么图中∠ADE是( )度.
- 3最近,你班同学就“太空探索是否值得”这一话题展开了一场讨论。请你根据下表提供的信息,用英语写一篇短文介绍讨论的情况。30
- 4关于工业地域的叙述,正确的是( )A.工业集聚产生了工业联系,形成工业地域B.工业分散使工业间距离拉大,联系不便,运
- 5下列关于硝化反应说法正确的是A.硝化反应是酯化反应,属于取代反应类型B.硝化反应中混合酸的配制是先加浓硫酸,再加浓硝酸C
- 6已知半径为5的圆的圆心在x轴上,圆心的横坐标是整数,且与直线4x+3y-29=0相切.(1)求圆的方程;(2)若直线ax
- 7233除以9的余数是______.
- 8对于数据3,3,2,3,6,3,10,3,6,3,2,(1)这组数据的众数是3,(2)这组数据的众数与中位数的数值不等,
- 9有一边长为5cm的正方体金属块,密度为ρ金属=8×103kg/m3,求:①此金属块的质量是多少?②放在水平地面上时,对地
- 10下列物质中,属于纯净物的是A.氧气B.果汁C.空气D.海水