数学52《平行四边形的判定》课件.ppt

1、2 2 平行四边形的判定平行四边形的判定1.1.会证明平行四边形的判定定理会证明平行四边形的判定定理.2.2.能运用平行四边形的判定定理进行简单的计算能运用平行四边形的判定定理进行简单的计算与证明与证明.3.3.能运用平行四边形的性质与判定定理进行比较能运用平行四边形的性质与判定定理进行比较简单的综合推理与证明简单的综合推理与证明.小明在家用细木棒钉制了一个平行四边形小明在家用细木棒钉制了一个平行四边形.第二天，小第二天，小明拿着自己动手做的平行四边形向同学们展示明拿着自己动手做的平行四边形向同学们展示.小辉却问：你凭什么确定这四边形就是平行四边形呢？小辉却问：你凭什么确定这四边形就是平行四边

2、形呢？大家都困惑了大家都困惑了你能帮助小明吗？你能帮助小明吗？对边平行对边平行边边对边相等对边相等对角相等对角相等角角邻角互补邻角互补对角线对角线互相平分互相平分平平行行四四边边形形平行四边形有那些性质？平行四边形有那些性质？1.1.两组对边分别平行的四边形是平行四边形两组对边分别平行的四边形是平行四边形2.2.两组对边分别相等的四边形是平行四边形两组对边分别相等的四边形是平行四边形3.3.一组对边平行且相等的四边形是平行四边形一组对边平行且相等的四边形是平行四边形4.4.对角线互相平分的四边形是平行四边形对角线互相平分的四边形是平行四边形5.5.两组对角分别相等的四边形是平行四边形两组对角分

3、别相等的四边形是平行四边形第第1 1是定义，不需证明，你能证明其他四个吗？试试吧是定义，不需证明，你能证明其他四个吗？试试吧.注意小组成员交流哦！注意小组成员交流哦！平行四边形的判定条件平行四边形的判定条件例例1 1 已知已知:如图如图,在四边形在四边形ABCDABCD中中,AB=CD,BC=DA.,AB=CD,BC=DA.求证求证:四边形四边形ABCDABCD是平行四边形是平行四边形.【分析分析】要证明四边形要证明四边形ABCDABCD是平行四是平行四边形边形.可转化证明两组对边分别平可转化证明两组对边分别平行行,从而作辅助线从而作辅助线,用全等三角形来证明相应的角相等用全等三角形来证明相应

4、的角相等.证明证明:连接连接AC.AB=CD,BC=DA,AC=CA,AC.AB=CD,BC=DA,AC=CA,ABCABCCDA(SSS).1=2,3=4.CDA(SSS).1=2,3=4.ABCD,CBAD.ABCD,CBAD.四边形四边形ABCDABCD是平行四边形是平行四边形.【定理定理】两组对边分别相等的四边形是平行四边形两组对边分别相等的四边形是平行四边形.BDCA1234【例题例题】已知已知:如图如图.求证求证:四边形四边形MNOPMNOP是平行四边形是平行四边形.【分析分析】这是一道综合性题目这是一道综合性题目,利用利用勾股定理和平行四边形的判定定理勾股定理和平行四边形的判定定

5、理进行计算性推理可获证进行计算性推理可获证.证明证明:(x-3)(x-3)2 2-(x-5)-(x-5)2 2=4=42 2 x=8.x=8.MN=5=PO.MN=5=PO.PM=3=ON.PM=3=ON.四边形四边形MNOPMNOP是平行四边形是平行四边形.OMNP45x-311-xx-5【跟踪训练跟踪训练】例例2 2 已知已知:如图如图,在四边形在四边形ABCDABCD中中,ABCD,AB=CD.,ABCD,AB=CD.求证求证:四边形四边形ABCDABCD是平行四边形是平行四边形.【分析分析】要证明四边形要证明四边形ABCDABCD是平行四是平行四边形边形.可转化证明两组对边分别相可转化

6、证明两组对边分别相等等,从而作辅助线从而作辅助线,用全等三角形来证明相应的边相等用全等三角形来证明相应的边相等.证明证明:连接连接AC.ABCD,AC.ABCD,1=2.AB=CD,AC=CA,1=2.AB=CD,AC=CA,ABCABCCDA(SAS).CDA(SAS).BC=DA.BC=DA.四边形四边形ABCDABCD是平行四边形是平行四边形.【定理定理】一组对边平行且相等的四边形是平行四边形一组对边平行且相等的四边形是平行四边形.BDCA12【例题例题】已知已知:如图如图,在四边形在四边形ABCDABCD中中,A=C,B=D.,A=C,B=D.求证求证:四边形四边形ABCDABCD是平

7、行四边形是平行四边形.【分析分析】要证明四边形要证明四边形ABCDABCD是平行四边形是平行四边形.可转化证明两组对边分别平行可转化证明两组对边分别平行.从而转化从而转化为相关的角关系来证明为相关的角关系来证明.证明证明:A=C,B=D,A+C+B+D=360A=C,B=D,A+C+B+D=360.2A+2B=360 2A+2B=360.A+B=180.A+B=180.ADBC.ADBC.同理同理,ABCD.,ABCD.四边形四边形ABCDABCD是平行四边形是平行四边形.BDCA【跟踪训练跟踪训练】例例3 3 已知已知:如图如图,在四边形在四边形ABCDABCD中中,对角线对角线AC,BDA

8、C,BD相交于点相交于点O,CO=AO,BO=DO.O,CO=AO,BO=DO.求证求证:四边形四边形ABCDABCD是平行四边形是平行四边形.【分析分析】要证明四边形要证明四边形ABCDABCD是平行四边形是平行四边形.可转化证明两可转化证明两组对边分别平行组对边分别平行,从而用全等三角形来证明相应的角相等从而用全等三角形来证明相应的角相等.证明证明:CO=AO,BO=DO,1=2,CO=AO,BO=DO,1=2,AODAODCOB(SAS).COB(SAS).3=4.ADCB.3=4.ADCB.同理同理,ABCD.,ABCD.四边形四边形ABCDABCD是平行四边形是平行四边形.【定理定理

9、】对角线互相平分的四边形是平行四边形对角线互相平分的四边形是平行四边形.BDCAO4321【例题例题】请你识别下列四边形哪些是平行四边形请你识别下列四边形哪些是平行四边形?为什么？为什么？A AD DC CB B1101107070110110A AB BC CD D12012060605 55 5A AB BC CD DO O5 55 54 44 4B BA AD DC C4.84.84.84.87.67.67.67.6【跟踪训练跟踪训练】1 1（成都（成都中考）已知四边形中考）已知四边形ABCDABCD，有以下四个条件：，有以下四个条件：ABCD ABCD AB=CD AB=CD BCAD

10、 BCAD BC=AD BC=AD 从这四个条件从这四个条件中任选两个，能使四边形中任选两个，能使四边形ABCDABCD成为平行四边形的选法种数成为平行四边形的选法种数共有（共有（）A.6A.6种种 B.5B.5种种 C.4C.4种种 D.3D.3种种C C2 2（常德（常德中考）如图，四边形中考）如图，四边形ABCDABCD中，中，AB/CDAB/CD，要使四，要使四边形边形ABCDABCD为平行四边形，则可添加的条件为为平行四边形，则可添加的条件为 （填一个（填一个即可）即可）.DB CA答案：答案：AB=CDAB=CD或或A=CA=C或或ADBCADBC等等3.3.已知已知:如图如图,在

11、在ABCDABCD中中,BF=DE.,BF=DE.求证求证:四边形四边形AFCEAFCE是平行四边形是平行四边形.分析分析:由已知的平行四边形和由已知的平行四边形和BF=DEBF=DE可知可知,CE=AF,CE=AF,则转化为利用则转化为利用一组对边平行且相等来证明一组对边平行且相等来证明.证明证明:四边形四边形ABCDABCD是平行四边形是平行四边形,DCAB,DC=AB.DCAB,DC=AB.DE=BF,CE=AF,DE=BF,CE=AF,四边形四边形AFCEAFCE是平行四边形是平行四边形.ABCDEF4.4.已知已知:如图如图,在在ABCDABCD中中,ABC,ABC的平分线与的平分线

12、与ADAD相交于点相交于点P.P.求证求证:PD+CD=BC.:PD+CD=BC.分析分析:要证明两条线段的和等于另一条线段要证明两条线段的和等于另一条线段,可以将可以将BCBC分割分割为两部分为两部分,来证明相应的线段相等来证明相应的线段相等.如将如将CDCD平移平移(过过P P作作CDCD的的平行线平行线)到到PEPE的位置的位置,则可利用等角对等边来证明则可利用等角对等边来证明PE=BE,PE=BE,从从而问题得证而问题得证.DBCAP证明证明:过点过点P P作作PECD,PECD,交交BCBC于点于点E.E.四边形四边形ABCDABCD是平行四边形是平行四边形,ABCD,ADBC.PE

13、CDAB,ABCD,ADBC.PECDAB,四边形四边形PDCEPDCE是平行四边形是平行四边形,1,13.3.PD=EC,PE=CD.PD=EC,PE=CD.1 12.32.32.2.PE=BE.PD+CD=EC+BE=BC.PE=BE.PD+CD=EC+BE=BC.DBCAP31E12 D DA AB BC CM MN NP PQ QO O5 5.已知已知:在平行四边形在平行四边形ABCDABCD中中,对角线对角线ACAC，BDBD相交于点相交于点O O，M M，N N，P P，Q Q分别是分别是OAOA，OB OB，OCOC，ODOD的中点的中点.求证：四边形求证：四边形MNPQMNPQ

14、是平行四边形，是平行四边形，证明：证明：在平行四边形在平行四边形ABCDABCD中，中，AO=COAO=CO，BO=DOBO=DO，M M，N N，P P，Q Q分别是分别是OAOA，OBOB，OCOC，ODOD的中点，的中点，OM=OPOM=OP，ON=OQON=OQ，四边形四边形MNPQMNPQ是平行四边形是平行四边形.1.1.会证明平行四边形的判定定理会证明平行四边形的判定定理.2.2.能运用平行四边形的判定定理进行简单的计算能运用平行四边形的判定定理进行简单的计算与证明与证明.3.3.能运用平行四边形的性质与判定定理进行比较能运用平行四边形的性质与判定定理进行比较简单的综合推理与证明简

15、单的综合推理与证明.通过本课时的学习，需要我们掌握：通过本课时的学习，需要我们掌握：雪地里的第一行脚印往往使几乎所有的后来者丧失了寻找更好的路径的勇气Unit 5 Can you come to my party?Can you can a can as a canner kn can can a can?你能像一个罐头制造商那样装罐头吗你能像一个罐头制造商那样装罐头吗？Who is the fastest?(谁最快？谁最快？)1 can助词助词 v.aux.(表示能力、功表示能力、功能能)能能,会会2 can名词 n.(食物食物)罐头罐头3 can及物动词及物动词 vt.把把(食品等食品等)

16、装罐装罐canner名词名词 n.罐头制罐头制造商造商Excuse me,can you come to my dancing party?Certainly,Id love like to.Sure,Id lovelike to.Of cause,Id lovelike to.A:Can you play basketball with us?prepare for an examB:Sorry,I cant.I A:Can you?B:Sorry,I cant.I go to the doctorA:Can you?B:Sorry,I cant.I meet my friendA:Can

17、you?B:Sorry,I cant.I have to have a piano lessonA:Can you?B:Sorry,.I have toB:Thanks for inviting/asking .help my parentsCan you come to my birthday party?Im sorry,I cant.I have the flu.How to accept an invitation Yes,Id love/like to.Certainly,Id love/like to.Sure,Id love/like to.Thanks for your inv

18、itation.Thanks for asking me.How to decline an invitation Im sorry,I cant.I have to Id love to,but I have to Sorry,I cant.Im going to the movies.Thanks for your invitation.Thank you for asking me.2a.Listen and circle can or cant.1.Jeff can/cant go to the party.2.Mary can/cant go to the party.3.May c

19、an/cant go to the party.4.Mei Ling can/cant go to the party.5.Paul can/cant go to the party.Can Jeff come to the party?No,he cant.Can Mary come to the party?Yes,she can.Can May come to the party?No,she cant.Can Meiling come to the party?No,she cant.Can Paul come to the party?Yes,he can.2b.Listen aga

20、in.Who cant go to the party?Why?Complete the chart.names reasonsJeffJeff might have to meet hisfriend on Saturday.MayMay has the flu.Mei Ling has the flu.Mei LingTape script Conversation 1 Anna:Hi,Jeff!Can you come to my party on Saturday?Jeff:Im sorry,Im not free.I might have to meet my friend on S

21、aturday.Conversation 2 Anna:Hello,Mary!Can you come to my party on Saturday?Mary:Id love to.Do I need to bring anything?Anna:No,Ill buy all the food and drinks.Conversation 3 Anna:May,can you come to my party tomorrow?May:Im afraid not.I have the flu.Anna:Oh,thats so bad.Well,drink lots of hot water

22、 and get lots of sleep.Conversation 4 Anna:Mei Ling,can you come to my party on Saturday?Mei Ling:Sorry,but Im not available.I must study for a math test.Anna:Ok.Good luck!Conversation 5 Anna:Hey,Paul.Can you come to my party on Saturday?Paul:sure.It sounds great.When will it start?Anna:Around 6:00

23、p.m.See you then.Paul:See you.2c Look at the reasons in the chart in 2b.Write some more.Then,Student A,invite your partner to do something.Student B,say you cant go and why.Reasons:1.Too much homework2.have to take part in the football match3.have to look after his little sister4.have to visit his g

24、randparents Hey,Dove.Can you go to the movies on Saturday?Im sorry,Im not available.I have too much homeworkthis weekend.2c.Pair workThats too bad.Maybe another time.Sure,Joe.Thanks for asking.1.Thats too bad.太遗憾了。表示遗憾或同情。太遗憾了。表示遗憾或同情。2.Maybe another time.也许换个时间吧。也许换个时间吧。或或Maybe next time.也许下一次吧也许下一

25、次吧3.another/the other/others/the others1)another another+n.(单数单数)三者中或无范围的另一个三者中或无范围的另一个 eg.This coat is too big.Please show me another one.2)the other one,the other 一个是一个是,另一个是另一个是.,表示两表示两者中的另一个者中的另一个 eg.I have two pens.One is black,the other is red.Explanation 3)others=other+n.(pl.),无范围的另一些无范围的另一些

26、someothers.“一些一些另一些另一些.”eg.Lei Feng was always ready to help others(=other+people)4)the others=the other+n.(pl.),有范围的另外有范围的另外一些一些,“其余所有的其余所有的”eg.There are sixty-two students in our class,one third are girls,the others(=the other students)are boys.注：注：another 另外的另外的,附加的附加的 eg.another three books=thre

27、e other/more books另外三本书另外三本书Hey,Tom.Can you go to the movies on Saturday?Im sorry,Im not available.I have to take part in the football matchThats too bad.Maybe another time.Sure,Joe.Thanks for asking.1.1.复习备考复习备考_2.2.帮助我的父母干家务帮助我的父母干家务_3.3.去看医生去看医生_ _ 4.4.见我朋友见我朋友_5.5.太多作业太多作业_6.6.谢谢你的邀请谢谢你的邀请_study

28、 for a test help my parents do houseworkgo to the doctormeet my friend too much homework thanks for your invitationTom:Hey,Jeff,can you come to my Christmas party?Jeff:When is it?Tom:Its on Saturday,December 24,at six oclock.Jeff:Great!Id love to.Tom:How about you,Lucy?Lucy:I am sorry,I cant.I am go

29、ing to the movies with my family.Can you come to?Christmas partySaturday,December 24,six oclockJeff:Sure/greatLucy:Sorrygo to the movies with my familyIts a Birthday Party!For whom:Lisa Time:Friday,October 15,at four-thirtyPlace:Lisas house,15th street Come and join us!Lucy:Hi,Tom,can you come to Lisas Birthday Party?Tom:is it?Lucy:Its at .Tom:is it?Lucy:Its in ,on .Tom:Great!Id love to.When On Friday,October 15 four-thirtyWhereLisas housethe 15th streetHomework 1.Make an invitation card for your friend.2.Write a conversation about invitation.