勾股定理及应用复习讲义.doc

专业好文档勾股定理及应用复习讲义 【一、知识点梳理：】1、勾股定理的内容与证明；2、勾股定理的逆定理的内容；勾股数的概念；3、用勾股定理及逆定理进行计算或推理或应用；【二、例题选用：】例1（1）在abc中，c90，a=6,c=10,则b= ，abc的面积为_（2）若三角形的三边长分别是x+1,x+2,x+3,则当x= 时，此三角形为直角三角形（3）已知在rtabc中，a、b为直角边,c为斜边，若a+b=14，c=10，则abc的面积是_ （第4题图）（4）如图所示的正方形是由边长为1的小正方形构成，连接三个格点构成abc，则abc的周长是 ，ac边上的高是 例2如图,在长方形abcd中,dc=5,在dc上存在一点e,沿直线ae把aed折叠,使点d恰好bc边上,设此点为f,若abf的面积为30,求折叠的aed的面积fedcba例3如图，公路mn和公路pq在点p处交汇，且qpn30，点a处有一所中学，ap160米，假设拖拉机行驶时，周围100米以内会受到噪音的影响，那么拖拉机在公路mn上沿pn方向行驶时，学校是否回受到噪声的影响？说明理由如果受影响，已知拖拉机的速度为18千米时，那么学校受影响的时间为多少秒？例4. 现有10个边长为1的正方形，排列形式如图，请把它们分割后拼接成一个新的正方形，要求：在图中用虚线画出分割线，并在图的正方形网格图（图中每个小正方形的边长均为1）中用实粗线画出拼接成的新正方形（说明：直接画出图形，不要求写分析过程）图1 图2 例4. 如图在四边形abcd中，dab=bcd=90，ab=ad，若这个四边形的面积是32，(1)求bc+cd的值；（2）求ac的值；3、如图坐标系中，矩形abco的边oa在x轴上，边oc在y轴上，点b的坐标为（1，3），沿对角线ac翻折，b点落在d点的位置，且ad交y轴于点e，求点d的坐标。abcdeoxy例5.如图（1）所示，直线l：y=kx+5k与x轴负半轴、y轴正半轴分别交于a、b两点。（1）、求点a的坐标；（2）、如图（2）所示，当oa=ob时，设q为线段ab延长线上一点，连接oq，过a、b两点分别作am oq于m，bn oq于n，若bn=3，求mn的长；（3）、如图（3），当k取不同的值时，点b在y轴的正半轴上运动，分别以ob、ab为边在第一、第二象限作等腰直角三角形obf和abe,连接ef交y轴于p点，问当点b在y轴上运动时，试猜想pb的长是否为定值，若是，请求出其值；若不是，请说明理由。【课后练习】一、选择1等腰三角形底边上的高为4cm，周长为16cm，则三角形面积 （ ）a14 b12 c10 d82下列各组线段中的三个长度：9，12，15；7，24，25； 32，42，52；3a，4a，5a（a0）；m2-n2，2mn，m2+n2（m，n为正整数，且mn）其中可以构成直角三角形的有（）a、2组 b、3组 c、4组 d、5组3如图，以直角三角形的三边作三个半圆，s1=30，s2=40，则 s3等于（ ）来源:a50 b60 c70 d804. 已知abc中，则它的三边之比为 （ ）a. b. c. d. 5. 已知等腰三角形的腰长为10，一腰上的高为6，则以底边为边长的正方形的面积为 （） a、40b、80c、40或360d、80或360二、填空6在abc中，c90，bc12，ab20，则ac_7直角三角形的周长为2，斜边长为2，则此直角三角形的面积为_8.等腰abc的腰长为10cm，底边长为16cm，则面积为_ ,腰上的高为 。9.在abc中，ab10，bc16，中线ad6，则ac_10.abc中,已知ab=15,ac=13,bc边上的高ad=12,bc的长是_.11.在长、宽都是3，高是8的长方体纸箱的外部, 一只蚂蚁从顶点a沿 纸箱表面爬到顶点b点，则它所行的最短路线的长是 .12如图，在rtabc中，b90，两条直角边分别为ab5，bc12，且在此三角形内有一点p到各边的距离都相等，这个距离的长是 13.如图，在rtabc中，c=90，bc=6cm，ac=8cm，按图中所示方法将bcd沿bd折叠，使点c落在ab边的c点，那么adc的面积是 14.在平面直角坐标系中，已知点a（，0），b（，0），点c在坐标轴上，且ac+bc=6，写出满足条件的所有点c的坐标 。15 如图，在四边形abcd中，adab2，a90， bc6，cd则adc的度数为 16若abc的边长a、b、c满足（a2+b2-c2）（a-b）=0，则abc形状是 第13题图第3题 第11题 第12题 第15题三、解答题17.如图，在rtabc中，c90，ac=12， bc9，ab的垂直平分线分别交ab、ac及bc的延长线于点d、e、f，求ce和cf的长18. 3、如图，有一块塑料矩形模板abcd，长为8cm，宽为4cm，将你手中足够大的直角三角板phf的直角顶点p落在ad边上（不与a、d重合），在ad上适当移动三角板顶点p，能否使你的三角板两直角边分别通过点b与点c？若能，请你求出这时ap的长；若不能，请说明理由19.如图，ab为一棵大树，在树上距地面10m的d处有两只猴子，它们同时发现地面上的c处有一筐水果，一只猴子从d处上爬到树顶a处，利用拉在a处的滑绳ac，滑到c处，另一只猴子从d处滑到地面b，再由b跑到c，已知两猴子所经过的路程都是15cm，求树高ab。20.如图，直线y=2x+6交y轴于点a，点b是直线上第一象限内的一个动点，点p是直线x=8上的一个动点，（1）求直线与坐标轴围成的三角形的面积；（2）若abp是等腰直角三角形，则求出点b的坐标；|x|k winger tuivasa-sheck, who scored two tries in the kiwis 20-18 semi-final win over england, has been passed fit after a lower-leg injury, while slater has been named at full-back but is still recovering from a knee injury aggravated against usa.both sides boast 100% records heading into the encounter but australia have not conceded a try since josh charnleys effort in their first pool match against england on the opening day.aussie winger jarryd hayne is the competitions top try scorer with nine, closely followed by tuivasa-sheck with eight.but it is recently named rugby league international federation player of the year sonny bill williams who has attracted the most interest in the tournament so far.the kiwi - with a tournament high 17 offloads - has the chance of becoming the first player to win the world cup in both rugby league and rugby union after triumphing with the all blacks in 2011.id give every award back in a heartbeat just to get across the line this weekend, said williams.the (lack of) air up there watch mcayman islands-based webb, the head of fifas anti-racism taskforce, is in london for the football associations 150th anniversary celebrations and will attend citys premier league match at chelsea on sunday.i am going to be at the match tomorrow and i have asked to meet yaya toure, he told bbc sport.for me its about how he felt and i would like to speak to him first to find out what his experience was.uefa hasopened disciplinary proceedings against cskafor the racist behaviour of their fans duringcitys 2-1 win.michel platini, president of european footballs governing body, has also ordered an immediate investigation into the referees actions.cska said they were surprised and disappointed by toures complaint. in a statement the russian side added: we found no racist insults from fans of cska. baumgartner the disappointing news: mission aborted.the supersonic descent could happen as early as sunda.the weather plays an important role in this mission. starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. the balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where our day-to-day weather lives. it will climb higher than the tip of mount everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. as he crosses the boundary layer (called the tropopause),e can expect a lot of turbulence.the balloon will slowly drift to the edge of space at 120,000 feet ( then, i would assume, he will slowly step out onto something resembling an olympic diving platform.they blew it in 2008 when they got caught cold in the final and they will not make the same mistake against the kiwis in manchester.five years ago they cruised through to the final and so far history has repeated itself here - the last try they conceded was scored by englands josh charnley in the opening game of the tournament.that could be classed as a weakness, a team under-cooked - but i have been impressed by the kangaroos focus in their games since then.they have been concentrating on the sort of stuff that wins you tough, even contests - strong defence, especially on their own goal-line, completing sets and a good kick-chase. theyve been great at all the unglamorous stuff that often