勾股定理及應(yīng)用復(fù)習(xí)講義

1、專業(yè)好文檔勾股定理及應(yīng)用復(fù)習(xí)講義 【一、知識(shí)點(diǎn)梳理：】1、勾股定理的內(nèi)容與證明；2、勾股定理的逆定理的內(nèi)容；勾股數(shù)的概念；3、用勾股定理及逆定理進(jìn)行計(jì)算或推理或應(yīng)用；【二、例題選用：】例1（1）在abc中，c90，a=6,c=10,則b= ，abc的面積為_（2）若三角形的三邊長分別是x+1,x+2,x+3,則當(dāng)x= 時(shí)，此三角形為直角三角形（3）已知在rtabc中，a、b為直角邊,c為斜邊，若a+b=14，c=10，則abc的面積是_ （第4題圖）（4）如圖所示的正方形是由邊長為1的小正方形構(gòu)成，連接三個(gè)格點(diǎn)構(gòu)成abc，則abc的周長是 ，ac邊上的高是 例2如圖,在長方形abcd中,dc=

2、5,在dc上存在一點(diǎn)e,沿直線ae把a(bǔ)ed折疊,使點(diǎn)d恰好bc邊上,設(shè)此點(diǎn)為f,若abf的面積為30,求折疊的aed的面積fedcba例3如圖，公路mn和公路pq在點(diǎn)p處交匯，且qpn30，點(diǎn)a處有一所中學(xué)，ap160米，假設(shè)拖拉機(jī)行駛時(shí)，周圍100米以內(nèi)會(huì)受到噪音的影響，那么拖拉機(jī)在公路mn上沿pn方向行駛時(shí)，學(xué)校是否回受到噪聲的影響？說明理由如果受影響，已知拖拉機(jī)的速度為18千米時(shí)，那么學(xué)校受影響的時(shí)間為多少秒？例4. 現(xiàn)有10個(gè)邊長為1的正方形，排列形式如圖，請(qǐng)把它們分割后拼接成一個(gè)新的正方形，要求：在圖中用虛線畫出分割線，并在圖的正方形網(wǎng)格圖（圖中每個(gè)小正方形的邊長均為1）中用實(shí)粗線畫

3、出拼接成的新正方形（說明：直接畫出圖形，不要求寫分析過程）圖1 圖2 例4. 如圖在四邊形abcd中，dab=bcd=90，ab=ad，若這個(gè)四邊形的面積是32，(1)求bc+cd的值；（2）求ac的值；3、如圖坐標(biāo)系中，矩形abco的邊oa在x軸上，邊oc在y軸上，點(diǎn)b的坐標(biāo)為（1，3），沿對(duì)角線ac翻折，b點(diǎn)落在d點(diǎn)的位置，且ad交y軸于點(diǎn)e，求點(diǎn)d的坐標(biāo)。abcdeoxy例5.如圖（1）所示，直線l：y=kx+5k與x軸負(fù)半軸、y軸正半軸分別交于a、b兩點(diǎn)。（1）、求點(diǎn)a的坐標(biāo)；（2）、如圖（2）所示，當(dāng)oa=ob時(shí)，設(shè)q為線段ab延長線上一點(diǎn)，連接oq，過a、b兩點(diǎn)分別作am oq于m

4、，bn oq于n，若bn=3，求mn的長；（3）、如圖（3），當(dāng)k取不同的值時(shí)，點(diǎn)b在y軸的正半軸上運(yùn)動(dòng)，分別以ob、ab為邊在第一、第二象限作等腰直角三角形obf和abe,連接ef交y軸于p點(diǎn)，問當(dāng)點(diǎn)b在y軸上運(yùn)動(dòng)時(shí)，試猜想pb的長是否為定值，若是，請(qǐng)求出其值；若不是，請(qǐng)說明理由?！菊n后練習(xí)】一、選擇1等腰三角形底邊上的高為4cm，周長為16cm，則三角形面積 （ ）a14 b12 c10 d82下列各組線段中的三個(gè)長度：9，12，15；7，24，25； 32，42，52；3a，4a，5a（a0）；m2-n2，2mn，m2+n2（m，n為正整數(shù)，且mn）其中可以構(gòu)成直角三角形的有（）a、2組

5、 b、3組 c、4組 d、5組3如圖，以直角三角形的三邊作三個(gè)半圓，s1=30，s2=40，則 s3等于（ ）來源:a50 b60 c70 d804. 已知abc中，則它的三邊之比為 （ ）a. b. c. d. 5. 已知等腰三角形的腰長為10，一腰上的高為6，則以底邊為邊長的正方形的面積為 （） a、40b、80c、40或360d、80或360二、填空6在abc中，c90，bc12，ab20，則ac_7直角三角形的周長為2，斜邊長為2，則此直角三角形的面積為_8.等腰abc的腰長為10cm，底邊長為16cm，則面積為_ ,腰上的高為 。9.在abc中，ab10，bc16，中線ad6，則ac

6、_10.abc中,已知ab=15,ac=13,bc邊上的高ad=12,bc的長是_.11.在長、寬都是3，高是8的長方體紙箱的外部, 一只螞蟻從頂點(diǎn)a沿 紙箱表面爬到頂點(diǎn)b點(diǎn)，則它所行的最短路線的長是 .12如圖，在rtabc中，b90，兩條直角邊分別為ab5，bc12，且在此三角形內(nèi)有一點(diǎn)p到各邊的距離都相等，這個(gè)距離的長是 13.如圖，在rtabc中，c=90，bc=6cm，ac=8cm，按圖中所示方法將bcd沿bd折疊，使點(diǎn)c落在ab邊的c點(diǎn)，那么adc的面積是 14.在平面直角坐標(biāo)系中，已知點(diǎn)a（，0），b（，0），點(diǎn)c在坐標(biāo)軸上，且ac+bc=6，寫出滿足條件的所有點(diǎn)c的坐標(biāo) 。15

7、 如圖，在四邊形abcd中，adab2，a90， bc6，cd則adc的度數(shù)為 16若abc的邊長a、b、c滿足（a2+b2-c2）（a-b）=0，則abc形狀是 第13題圖第3題 第11題 第12題 第15題三、解答題17.如圖，在rtabc中，c90，ac=12， bc9，ab的垂直平分線分別交ab、ac及bc的延長線于點(diǎn)d、e、f，求ce和cf的長18. 3、如圖，有一塊塑料矩形模板abcd，長為8cm，寬為4cm，將你手中足夠大的直角三角板phf的直角頂點(diǎn)p落在ad邊上（不與a、d重合），在ad上適當(dāng)移動(dòng)三角板頂點(diǎn)p，能否使你的三角板兩直角邊分別通過點(diǎn)b與點(diǎn)c？若能，請(qǐng)你求出這時(shí)ap的

8、長；若不能，請(qǐng)說明理由19.如圖，ab為一棵大樹，在樹上距地面10m的d處有兩只猴子，它們同時(shí)發(fā)現(xiàn)地面上的c處有一筐水果，一只猴子從d處上爬到樹頂a處，利用拉在a處的滑繩ac，滑到c處，另一只猴子從d處滑到地面b，再由b跑到c，已知兩猴子所經(jīng)過的路程都是15cm，求樹高ab。20.如圖，直線y=2x+6交y軸于點(diǎn)a，點(diǎn)b是直線上第一象限內(nèi)的一個(gè)動(dòng)點(diǎn)，點(diǎn)p是直線x=8上的一個(gè)動(dòng)點(diǎn)，（1）求直線與坐標(biāo)軸圍成的三角形的面積；（2）若abp是等腰直角三角形，則求出點(diǎn)b的坐標(biāo)；|x|k winger tuivasa-sheck, who scored two tries in the kiwis 20-

9、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

10、 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 att

11、racted 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 acr

12、oss 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

13、 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 pla

14、tini, 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 disappo

15、inting 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 capsul

16、e 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) an

17、d 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 2

18、008 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

19、 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