题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052229-71359.png)
(1) 求证:CE∥平面PAB;
(2) 求PA与平面ACE所成角的大小;
(3) 求二面角E-AC-D的大小.
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052229-90439.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052229-23187.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052229-23187.png)
解析
试题分析:(1)证明:取PA的中点F,连结FE、FB,则
FE∥BC,且FE=
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052229-90439.png)
∴CE∥BF,而BFÌ平面PAB,∴CE∥平面PAB.
(2) 解:取 AD的中点G,连结EG,则EG∥AP,问题转为求EG与平面ACE所成角的大小.又设点G到平面ACE的距离为GH,H为垂足,连结EH,则∠GEH为直线EG与平面ACE所成的角.现用等体积法来求GH.
∵VE-AGC=
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052229-29965.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052229-29965.png)
又AE=
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052230-28345.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052230-30818.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052229-23187.png)
∴VG-AEC=
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052229-29965.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052230-37373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052229-29965.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052229-23187.png)
在Rt△EHG中,sin∠GEH=
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052230-51445.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052229-23187.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052229-23187.png)
(3) 设二面角E-AC-D的大小为a.
由面积射影定理得cosa=
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052230-75105.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052229-23187.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052229-23187.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052229-23187.png)
点评:本题还可利用空间向量求解,利用AB,AD,AP两两垂直,以A为原点建立坐标系,根据线段长度写出各点坐标,带入相应的公式计算求角
核心考点
试题【(本小题满分12分)如图,四棱锥P-ABCD的底面ABCD是直角梯形,∠DAB=∠ABC=90o,PA⊥底面ABCD,PA=AB=AD=2,BC=1,E为PD的】;主要考察你对线线角等知识点的理解。[详细]
举一反三
如图,已知三棱锥A-BPC中,AP⊥PC,AC⊥BC,M为AB中点,D为PB中点,且△PMB为正三角形.
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052221-55747.png)
(1)求证:DM∥平面APC;
(2)求证:平面ABC⊥平面APC;
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052218-23536.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052218-89445.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052218-75399.png)
①若
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052219-87493.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052219-81973.png)
A.①是真命题,②是假命题 | B.①是假命题,②是真命题 |
C.①、②都是真命题 | D.①、②都是假命题 |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052208-16145.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052208-29240.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052208-81563.png)
(Ⅰ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052208-39801.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052209-78270.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052209-76953.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052204-40017.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052204-21124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052204-40017.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052204-21124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052204-28182.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052204-40017.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052204-28182.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052204-21124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052204-40017.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052204-21124.png)
A.相交或平行 | B.相交或异面 |
C.平行或异面 | D.相交﹑平行或异面 |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052158-48149.png)
求证:(1)平面AMD∥平面BPC;(2)平面PMD^平面PBD.
最新试题
- 1已知椭圆的右顶点为A,离心率e=12,过左焦点F(-1,0)作直线l与椭圆交于点P,Q,直线AP,AQ分别与直线x=-4
- 2宪法是国家的根本大法,是因为 ①宪法是普通法律的总和②宪法具有最高的法律效力③宪法规定国家生活的根本问题④宪法的制
- 3(Ⅰ)求函数的最大值和最小正周期;w.w.w.k.s.5.u.c.o.m
- 4在等边三角形ABC中,∠B和∠C的角平分线相交于点O,则∠BOC等于 [ ]A.100°B.110°C.120°
- 5They said to us, “Are you afraid to leave this house ?” They
- 6The young mother save her son though he was infected
- 7下列离子方程式正确的是( )A.H2O2 + 2OH-2H2O + O2↑B.2MnO4- + H2O2 + 6H+
- 8下面是水的密度随温度变化的示意图。请根据图示,写出相关结论。 _____________________________
- 9阅读材料,回答问题。材料一 “行仁政而王,莫之能御也。”;“处无为之事,行不言之教。”;“明法者强,慢法者弱。”材料二
- 10(10分)一辆汽车沿着平直的道路行驶,遇有紧急情况而刹车,刹车后轮子只滑动不滚动,从刹车开始到汽车停下来,汽车前进12米
热门考点
- 1Bethune invented tools _____ doctors still use today.[ ]
- 2用观察的标本图象偏向于视野的右上角,若要移到视野中央,则应将玻片标本往什么方向移动( )A.左下方B.右下方C.左上方
- 3湖南国家地级公园是指( )A.衡山B.岳麓山C.韶山D.莨山
- 4已知函数是正比例函数,则= .
- 5从化学知识的学习中,我们也可以学到做人做事的道理。比如两性氧化物,从悲观的角度看是不知“何去何从”,从乐观的角度去看是“
- 6有一瓶14%的氢氧化钾溶液,加热蒸发掉100g水后,得到28%的氢氧化钾溶液80mL,所得溶液的浓度为 A.5mo
- 7有专家指出:太平天国运动的进步性在于“试图从土地所有制方面解决占中国绝大多数人口的农民的土地问题”。下列各项能够论证这一
- 8曼德拉是公认的伟大政治家,他以非暴力方式实现了南非的种族和解,创建了各种族和谐相处的新南非。他留下的以忍让、博爱、宽容、
- 9下列有关阿伏加德罗常数(NA)的说法错误的是( )A.32gO2所含的原子数目为NAB.0.5molH2O含有的原子数
- 10下列物质中,含有氧分子的是A.过氧化氢B.液氧C.二氧化碳D.二氧化锰