勾股定理講義

1、專業(yè)好文檔 新思敏教育小班輔導(dǎo)講義 2014年3月8日教師耿慧靜班級(jí)八年級(jí)（下）授課時(shí)間 10：00-12:00授課科目數(shù) 學(xué)授課課題勾股定理課型鞏固教學(xué)目標(biāo) 1、 知識(shí)目標(biāo)：學(xué)會(huì)勾股定理以及逆定理；2、 能力目標(biāo)：掌握勾股定理及其逆定理的應(yīng)用；3、情感態(tài)度與價(jià)值觀：熟練掌握實(shí)際問(wèn)題中應(yīng)用勾股定理。教學(xué)重點(diǎn)和難點(diǎn)1、 重點(diǎn)：學(xué)會(huì)勾股定理以及逆定理；2、 難點(diǎn)：理解并掌握勾股定理及其逆定理的應(yīng)用。本章重要知識(shí)點(diǎn)1.勾股數(shù) 中，為正整數(shù)時(shí)，稱，為一組勾股數(shù)記住常見的勾股數(shù)可以提高解題速度，如；等用含字母的代數(shù)式表示組勾股數(shù)：（為正整數(shù)）；（為正整數(shù)） ；（，為正整數(shù)）。2.勾股定理及其逆定理的應(yīng)用

2、勾股定理及其逆定理在解決一些實(shí)際問(wèn)題或具體的幾何問(wèn)題中，是密不可分的一個(gè)整體通常既要通過(guò)逆定理判定一個(gè)三角形是直角三角形，又要用勾股定理求出邊的長(zhǎng)度，二者相輔相成，完成對(duì)問(wèn)題的解決常見圖形：經(jīng)典題型題型一：直接考查勾股定理 例.在中，（1）已知，求的長(zhǎng)； 已知，求的長(zhǎng)。題型二：應(yīng)用勾股定理建立方程例.在中，于，已知直角三角形的兩直角邊長(zhǎng)之比為，斜邊長(zhǎng)為，則這個(gè)三角形的面積為已知直角三角形的周長(zhǎng)為，斜邊長(zhǎng)為，則這個(gè)三角形的面積為分析：在解直角三角形時(shí)，要想到勾股定理，及兩直角邊的乘積等于斜邊與斜邊上高的乘積有時(shí)可根據(jù)勾股定理列方程求解例.如圖中，求的長(zhǎng)分析：此題將勾股定理與全等三角形的知識(shí)結(jié)合起

3、來(lái)例4.如圖，,分別以各邊為直徑作半圓，求陰影部分面積 題型三：實(shí)際問(wèn)題中應(yīng)用勾股定理例5.如圖有兩棵樹，一棵高，另一棵高，兩樹相距，一只小鳥從一棵樹的樹梢飛到另一棵數(shù)的樹梢，至少飛了題型四：應(yīng)用勾股定理逆定理，判定一個(gè)三角形是否是直角三角形例6.已知三角形的三邊長(zhǎng)為，判定是否為，例7.三邊長(zhǎng)為，滿足，的三角形是什么形狀？題型五：勾股定理與勾股定理的逆定理綜合應(yīng)用例8.已知中，邊上的中線，求證：練習(xí)題1. 下面幾組數(shù):7,8,9；12,9,15；m2 + n2, m2n2, 2mn（m，n均為正整數(shù),mn）；,.其中能組成直角三角形的三邊長(zhǎng)的是( )a. b. c. d. 2. 三角形的三邊長(zhǎng)

4、為,則這個(gè)三角形是( ) a. 等邊三角形 b. 鈍角三角形 c. 直角三角形 d. 銳角三角形. 3已知一個(gè)直角三角形的兩邊長(zhǎng)分別為3和4，則第三邊長(zhǎng)是（）a5 b25cd5或4已知rtabc中，c=90，若a+b=14cm，c=10cm，則rtabc的面積是（）a. 24cm2b. 36cm2 c. 48cm2 d. 60cm25直角三角形中一直角邊的長(zhǎng)為9，另兩邊為連續(xù)自然數(shù)，則直角三角形的周長(zhǎng)為（）a 121 b120 c90 d不能確定abefdc第10題圖6.已知，如圖，長(zhǎng)方形abcd中，ab=3，ad=9，將此長(zhǎng)方形折疊，使點(diǎn)b與點(diǎn)d重合，折痕為ef，則abe的面積為（）a.6b

5、.8c.10d.127. 四根小木棒的長(zhǎng)分別為5cm，8cm，12cm，13cm，任選三根組成三角形，其中有 個(gè)直角三角形.8. 如圖8，有一塊直角三角形紙片，兩直角邊ac=6cm，bc=8cm，現(xiàn)直角邊沿直線ad折疊，使它落在斜邊ab上，且與ae重合，則cd的長(zhǎng)為 9. 一只螞蟻沿直角三角形的邊長(zhǎng)爬行一周需2秒，如果將直角三角形的邊長(zhǎng)擴(kuò)大1倍，那么這只螞蟻再沿邊長(zhǎng)爬行一周需 （ ）.（a）6秒 （b）5秒 （c）4秒 （d）3秒10. 我國(guó)古代數(shù)學(xué)家趙爽“的勾股圓方圖”是由四個(gè)全等的直角三角形與中間的一個(gè)小正方形拼成的一個(gè)大正方形（如圖1所示），如果大正方形的面積是25，小正方形的面積是1，

6、直角三角形的兩直角邊分別是a、b，那么 的值為 （ ）.（a）49 （b）25 （c）13 （d）1本次課后作業(yè)：主任簽字: 新思敏教育總部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 aggravate

7、d 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-s

8、heck 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

9、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 footbal

10、l 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 experie

11、nce 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

12、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

13、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

14、.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 12

15、0,000 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

16、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 concentrat

17、ing 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 goes unnoticed in the stands but not by your team-mates.it is as though their entire tourn

18、ament has been preparation for the final.in johnathan thurston, cooper cronk, cameron smith and either billy slater or greg inglis at full-back they have a spine that is unmatched in rugby league. they have played in so many high-pressure games - a priceless asset going into saturday.the kiwis are a

19、 lot less experienced but winning a dramatic match like their semi-final against england will do wonders for their confidence.they defeated australia in the four nations final in 2010 and the last world cup, and know they can rise to the big occasion.winger tuivasa-sheck, who scored two tries in the

20、 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

21、 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 w

22、ho 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

23、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 goin

24、g 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.

25、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 t

26、he 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, w

27、ith 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 kilo

28、meters) 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 bl

29、ew 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