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＞＞＞三棱锥P-ABC，底面ABC为边长为23的正三角形，平面PBC⊥平面ABC，P..
三棱锥P-ABC，底面ABC为边长为23的正三角形，平面PBC⊥平面ABC，PB=PC=2，D为AP上一点，AD=2DP，O为底面三角形中心．（Ⅰ）求证DO∥面PBC；（Ⅱ）求证：BD⊥AC；（Ⅲ）求面DOB截三棱锥P-ABC所得的较大几何体的体积．
题型：解答题难度：中档来源：不详
（本小题满分12分）证明：（Ⅰ）连接AO并延长交BC于点E，连接PE、DO．--------------（1分）∵O为正三角形ABC的中心，∴AO=2OE，又AD=2DP，∴DO∥PE，--------------（2分）∵DO?平面PBC，PE?平面PBC--------------（3分）∴DO∥面PBC．--------------（4分）（Ⅱ）∵PB=PC，且E为BC中点，∴PE⊥BC，又平面PBC⊥平面ABC，∴PE⊥平面ABC．--------------（5分）由（Ⅰ）知，DO∥PE，∴DO⊥平面ABC，∴DO⊥AC--------------（6分）连接BO，则AC⊥BO，又DO∩BO=O，∴AC⊥平面DOB，--------------（7分）∴AC⊥BD．--------------（8分）（Ⅲ）连接BO并延长交AC于点F，连接DF，则面DOB将三棱锥P-ABC截成三棱锥D-ABF和四棱锥B-DFCP两个几何体．--------------（9分）VD-ABF=13×S△ABF×DO=13×323×23=33-----------（10分）VP-ABC=13×S△ABC×PE=13×33=3--------------（11分）∴所截较大部分几何体的体积为233．--------------（12分）
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据魔方格专家权威分析，试题“三棱锥P-ABC，底面ABC为边长为23的正三角形，平面PBC⊥平面ABC，P..”主要考查你对&&直线与平面平行的判定与性质&&等考点的理解。关于这些考点的“档案”如下：
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因为篇幅有限，只列出部分考点，详细请访问。
直线与平面平行的判定与性质
线面平行的定义：
若直线和平面无公共点，则称直线和平面平行。
图形表示如下：
线面平行的判定定理：
平面外一条直线与此平面内一条直线平行，则该直线与此平面平行。 线线平行线面平行
符号语言：
&线面平行的性质定理：
如果一条直线和一个平面平行，则过这条直线的任一平面与此平面的交线与该直线平行。 线面平行线线平行
&符号语言：
&证明直线与平面平行的常用方法：
(l)反证法，即&(2)判定定理法，即&(3)面面平行的性质定理，即&(4)向量法，平面外的直线的方向向量n与平面的法向量n垂直，则直线与平面平行，即
发现相似题
与“三棱锥P-ABC，底面ABC为边长为23的正三角形，平面PBC⊥平面ABC，P..”考查相似的试题有：
2654366208182589352673622660563322401）已知：如图1,三角形ABC是圆O的内接正三角形,点P为弧BC上一动点,求证PA=PB+PC.._百度作业帮
1）已知：如图1,三角形ABC是圆O的内接正三角形,点P为弧BC上一动点,求证PA=PB+PC..
1）已知：如图1,三角形ABC是圆O的内接正三角形,点P为弧BC上一动点,求证PA=PB+PC..
以P为圆心,PB为半径画圆,交AP于D,连接BD则：△PBE为正三角形即：PD=PB∵∠ADB=180-60=120º,∠CPB=60+60=120º∴∠ADB=∠CPB& & & ①∵∠BAD=∠BCP（对应同一段圆弧）&②由①②得：∠ABD=∠CBP& & ③& & & & ∵△ABC是正三角形∴AB=CB& & & & & & & & & & &④综合②③④得：∴△ABD≌△CBP（ASA）∴AD=CP∴PA=PD+AD=PB+PC&
没图，没法解已知直角三角形ABC，∠ABC=90°，AB=3，BC=5，以AC为边向外作正方形ACEF，则这个正方形的中心O到点B的距离为______．
如图，延长BA到D，使AD=BC，连接OD，OA，OC，∵四边形ACEF是正方形，∴∠AOC=90°，∵∠ABC=90°，∵∠ABC+∠AOC=180°，∴∠BCO+∠BAO=180°，∠BCO=∠DAO，又∵CO=AO，在△BCO与△DAO中，
∠BCO=∠DAO
，∴△BCO≌△DAO（SAS），∴OB=OD，∠BOC=∠DOA，∴∠BOD=∠COA=90°，∴△BOD是等腰直角三角形，∴BD=
OB，∵BD=AB+AD=AB+BC=8，∴OB=4
，故答案为4
Abraham Lincoln was born in Kentucky on February 12, 1809. When he was a small boy, his family moved to Indiana. Here, his mother taught him to read and write. Lincoln had very little formal education, but he became one of the best-educated men of the Great West. When Lincoln was a young man, his family moved to the new state of Illinois. Lincoln had to make a living at an early age, but in his spare time he studied law. He soon became one of the best-known lawyers in the state capital at Springfield, Illinois. It was here that Lincoln became famous for his debates with Stephen A. Douglas on the problem of slavery (奴隶制度). In 1860, Lincoln was elected President of the United States. He was the candidate of the new Republican Party. This party is against the creation of new slave states. Soon after his election, some of the Southern states quit from the Union and set up the Confederate States of America(美利坚联盟国). This action resulted in the terrible Civil War which lasted from 1861 to 1865. On January 1,1863, during the war, Lincoln published his famous Emancipation Proclamation(解放宣言). In this file, Lincoln announced that all the slaves were to be free from that day. In 1865, after the war ended, another file was added to end the slavery everywhere in the United States. Early in 1865, the Civil War came to an end with the defeat of the South by the North. Only a few days after the end of the War, Lincoln was shot by an actor named John Wilkes Booth. The President died on April 14, 1865. In his death, the world lost one of the greatest men of all time.小题1:Who taught Lincoln to read and write in his childhood?
(no more than 10 words) (2 marks)小题2:When did Lincoln become the president of the U.S.?
(no more than 3 words)
(2 marks)小题3:What does the underlined phrase “this action” in Paragraph Three refer to? (no more than 20 words)
(3 marks)小题4:How did the Civil War come to an end?
(no more than 10 words)
阅读短文，并按照题目要求用英语回答问题。Denielle Steel, America"s sweetheart, is one of the hardest working women in the book business. Unlike other productive authors who write one book at a time, she can work on up to five. Her research comes before writing takes at least three years. Once she has fully studied her subjects, she can spend twenty hours nonstop at her desk. Denielle Steel comes from New York and was sent to France for her education. After graduation, she worked in the public relations and advertising industries. Later she started a job as a writer which she was best fit for. Her achievements are unbelievable, 390 million copies of books in print, nearly fifty New York Times best-selling novels, and a series of “Max and Martha" picture books for children to help them deal with the real-life problem of death, new babies and new schools. Her book published in 1998 about the death of her was shot to the top of the New York Times best-selling list as soon as it came out. Twenty-eight of her books have been made into films. She is listed in the Guinness Books of World Records for one of her books being the Times best-seller for 381
weeks straight. Not content with a big house, a loving family, and a view of the Golden Gate Bridge, Denielle Steel considers her readers to be the most important resource and has kept in touch with them by-email. While she is often compared to the heroines of her own invention, her life is undoubtedly much quieter. But if she does have anything in common with them, it is her strength of will and her inimitable
style. There is only one, Denielle Steel!小题1:What is the main idea of the passage? (No more than 10 words)小题2:Please explain the underlined word "content" in English. (No more than 5 words)_______________________________________________________________________________小题3:What may children know after they have read "Max and Martha" picture books? (No more
than 20 words)_______________________________________________________________________________小题4:List at least three Danielle Steel"s achievements in book business? (No more than 30 words)_______________________________________________________________________________小题5:Why aid Danielle Steel value her readers a lot? (No more than 25 words)_______________________________________________________________________________
阅读下面短文并回答问题，然后将答案写到答题卡相应的位置上(请注意问题后的词数要求)[1] Sooner or later everyone has to write something-a thank-you note, a report at a meeting, a complaint or an apology. If you have writing assignment(作业) in school, or if you still fear to put pen to paper, facing that empty page is almost as frightening as you are facing a tiger. How to write it? There is no mystery. Clear writing is just clear thinking. Here are some techniques for you.[2] Thinking on paperSit down with a pencil and paper or at the computer screen and start outlining(概述，略述) what you want to say, why it is important, why it matters, and what its impact is on the reader. Just get the ideas down. The next step is to go back and put them in order.[3] Writing first sentenceTry to make your first sentence catch the reader’s eyes, because ________, the reader is not going to read on. Get a good, clear lead sentence that summarizes your points and answers the reader’s question “What is in it for me?” if you can not do it in one sentence, then do it in two or three but keep them short.[4] Remembering the readerShort, simple words are better than long words. Short sentences are better than long sentences. Remember that the goal is to communicate, not to express yourselves. Most people are so devoted to what they want to say that they forget somebody else has to be able to read it. Too much information makes you lose readers before they get to the meat(实质) of what you want to say.[5] Reading and rewritingRead out what you have written loud, and listen for any awkward(笨拙的) sentences. All good writers read, then rewrite. Back off a little bit from what you are writing. It is an old standard, but if you can, write something and come back a day later.小题1:What is the best title for the passage? (no more than 8 words)____________________________________________________________________________小题2:Which of the techniques do you think is the best for you? Why? (within 15 words)____________________________________________________________________________小题3:Fill in the blank in Paragraph 3 with proper words. (within 5 words)____________________________________________________________________________小题4:What’s the last step to write a better writing according to the passage? (within three words)____________________________________________________________________________小题5:What does the underlined word “it” (paragraph 2) probably refer to? (five words)____________________________________________________________________________
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旗下成员公司解：（1）①证法一∵△ABD与△ACE均为等边三角形，∴AD=AB，AC=AE，且∠BAD=∠CAE=60°，∴∠BAD+∠BAC=∠CAE+∠BAC，即∠DAC=∠BAE，∴△ABE≌△ADC．证法二：∵△ABD与△ACE均为等边三角形，∴AD=AB，AC=AE，且∠BAD=∠CAE=60°，∴△ADC可由△ABE绕着点A按顺时针方向旋转60°得到，∴△ABE≌△ADC，②120°，90°，72°．（2）①．②证法一：依题意，知∠BAD和∠CAE都是正n边形的内角，AB=AD，AE=AC，∴∠BAD=∠CAE=，∴∠BAD﹣∠DAE=∠CAE﹣∠DAE，即∠BAE=∠DAC，∴△ABE≌△ADC，∴∠ABE=∠ADC，∵∠ADC+∠ODA=180°，∴∠ABO+∠ODA=180°，∵∠ABO+∠ODA+∠DAB+∠BOC=360°，∴∠BOC+∠DAB=180°，∴∠BOC=180°﹣∠DAB=；证法三：同上可证△ABE≌△ADC．∴∠ABE=∠ADC．∵∠BOC=180°﹣（∠ABE+∠ABC+∠ACB+∠ACD），∴∠BOC=180°﹣（∠ADC+∠ABC+∠ACB+∠ACD），∵∠ABC+∠ACB=180°﹣∠BAC，∠ADC+∠ACD=180°﹣∠DAC，∴∠BOC=180°﹣（360°﹣∠BAC﹣∠DAC），∴∠BOC=180°﹣∠BAD=；证法四：同上可证△ABE≌△ADC．∴∠AEB=∠ACD．如图，连接CE，∵∠BEC=∠BOC+∠OCE，∴∠AEB+∠AEC=∠BOC+∠ACD﹣∠ACE，∴∠BOC=∠AEC+∠ACE．即∠BOC=180°﹣∠CAE=．
请选择年级七年级八年级九年级请输入相应的习题集名称(选填)：
科目：初中数学
如图（1），在Rt△ABC的边AB的同侧，分别以三边为直径作三个半圆，大半圆以外的两部分面积分别为S1、S3，三角形的面积为S2；如图（2），两个反比例函数和在第一象限内的图象如图所示，点P在的图象上，PC⊥x轴于点C，PD⊥y轴于点D，交的图象于分别于点A，B，当点P在的图象上运动时，△BOD，四边形OAPB，△AOC的面积分别为S1、S2、S3；如图（3），点E为?ABCD边AD上任意一点，三个三角形的面积分别为S1、S2、S3；如图（4），梯形ABCD中，AB∥CD，∠DAB+∠ABC=90°，AB=2CD，以AD、DC、CB为边作三个正方形的面积分别为S1、S2、S3．在这四个图形中满足S1+S3=S2有（填序号）．
科目：初中数学
如图，一架大型运输飞机从起飞开始到飞行10小时的时候，某空军加油飞机接到命令立即给运输飞机进行空中加油，设运输飞机的油箱余油量为Q1（吨），加油飞机从开始加油到加油结束的加油油箱耗油量为Q2（吨），运输飞机从起飞开始的飞行时间为t（小时），Q1（吨）、Q2（吨）与t（小时）之间的函数关系图象如图所示，若加油飞机与运输飞机每小时的耗油量相同，且运输飞机从起飞开始到降落一直保持匀速飞行，请结合图象，解答下列问题．（1）求运输飞机起飞时油箱的油量；（2）求运输飞机从起飞开始油箱余油量Q1（吨）与飞行时间t（小时）之间的函数关系式；（3）运输飞机加油后，以原来的速度继续飞行，据测算到达目的地还需要15小时，问油箱中的油料是否够用？请说明理由．
科目：初中数学
（2012?河北）如图，点E是线段BC的中点，分别以BC为直角顶点的△EAB和△EDC均是等腰三角形，且在BC同侧．（1）AE和ED的数量关系为AE=ED；AE和ED的位置关系为AE⊥ED；（2）在图1中，以点E为位似中心，作△EGF与△EAB位似，点H是BC所在直线上的一点，连接GH，HD．分别得到图2和图3．①在图2中，点F在BE上，△EGF与△EAB的相似比1：2，H是EC的中点．求证：GH=HD，GH⊥HD．②在图3中，点F在的BE延长线上，△EGF与△EAB的相似比是k：1，若BC=2，请直接写CH的长为多少时，恰好使GH=HD且GH⊥HD（用含k的代数式表示）．
科目：初中数学
如图1，是由一些棱长为1cm的小正方体组合成的简单几何体．（1）该几何体的主视图如图2，请在图3、图4中分别画出它的左视图和俯视图；（2）该几何体的表面积（含下底面）为cm2．
科目：初中数学
题型：解答题
如图，一架大型运输飞机从起飞开始到飞行10小时的时候，某空军加油飞机接到命令立即给运输飞机进行空中加油，设运输飞机的油箱余油量为Q1（吨），加油飞机从开始加油到加油结束的加油油箱耗油量为Q2（吨），运输飞机从起飞开始的飞行时间为t（小时），Q1（吨）、Q2（吨）与t（小时）之间的函数关系图象如图所示，若加油飞机与运输飞机每小时的耗油量相同，且运输飞机从起飞开始到降落一直保持匀速飞行，请结合图象，解答下列问题．（1）求运输飞机起飞时油箱的油量；（2）求运输飞机从起飞开始油箱余油量Q1（吨）与飞行时间t（小时）之间的函数关系式；（3）运输飞机加油后，以原来的速度继续飞行，据测算到达目的地还需要15小时，问油箱中的油料是否够用？请说明理由．知识点梳理
的性质:1.正方形具有、、矩形、菱形的一切性质。2.正方形的四条边都相等，邻边垂直，对边平行。3.正方形的四个角都是直角。4.正方形的对角线相等且互相垂直平分，每一条对角线平分一组对角。5.正方形是轴对称图形，它有4条对称轴。6.正方形的一条对角线把正方形分成两个全等的等腰直角三角形，对角线与边的夹角是45°。
判定：&&(1)三组对应边分别相等的两个三角形全等(简称SSS或“边边边”)，这一条也说明了三角形具有稳定性的原因。&&(2)有两边及其夹角对应相等的两个三角形全等(SAS或“边角边”)。&&(3)有两角及其夹边对应相等的两个三角形全等(ASA或“角边角”)。&&(4)有两角及一角的对边对应相等的两个三角形全等(AAS或“角角边”)&&(5)直角三角形全等条件有：斜边及一直角边对应相等的两个直角三角形全等(HL或“斜边，直角边”)&所以，SSS,SAS,ASA,AAS,HL均为判定三角形全等的定理。注意：在全等的判定中，没有AAA和SSA，这两种情况都不能唯一确定三角形的形状。性质：&&(1)的对应角相等。&&(2)全等三角形的对应边相等。&&(3)全等三角形的对应边上的高对应相等。&&(4)全等三角形的对应角的角平分线相等。&&(5)全等三角形的对应边上的中线相等。&&(6)全等相等。&&(7)全等三角形周长相等。&&(8)全等三角形的对应角的相等。
：直角两直角边的平方和等于斜边的平方，即如果直角三角形的两直角边长分别为a,b,斜边长为c，那么a?+b?=c?（勾股定理公式）
整理教师:&&
举一反三（巩固练习，成绩显著提升，去）
根据问他()知识点分析，
试题“已知直角三角形ABC，∠ABC=90°，AB=3，BC=5，...”，相似的试题还有：
如图，Rt△ABC中，∠C=90°，以斜边AB为边向外作正方形ABDE，且正方形对角线交于点O，连接OC，已知AC=5，OC=6\sqrt{2}，则另一直角边BC的长为_____．
如图，Rt△ABC中，∠C=90&，以斜边AB为边向外作正方形ABDE，且正方形对角线交于点O，连接OC，已知AC=5，OC=6，则另一直角边BC的长为()．
如图，Rt△ABC中，∠C=90&，以斜边AB为边向外作正方形ABDE，且正方形对角线交于点O，连接OC，已知AC=5，OC=6，则另一直角边BC的长为()．