第一篇:数学八年级下《命题与证明》复习测试题(答案)
命题与证明
一、选择题
1.下列语句中,属于命题的是().
(A)直线AB和CD垂直(B)过线段AB的中点C画AB的垂线
(C)同旁内角不互补,两直线不平行(D)连结A,B两点
2.下列命题中,属于假命题的是()
(A)若a⊥c,b⊥c,则a⊥b(B)若a∥b,b∥c,则a∥c
(C)若a⊥c,b⊥c,则a∥b(D)若a⊥c,b∥a,则b⊥c
3.下列四个命题中,属于真命题的是().
(A)互补的两角必有一条公共边(B)同旁内角互补(C)同位角不相等,两直线不平行(D)一个角的补角大于这个角
4.命题“垂直于同一条直线的两条直线互相平行”的题设是().
(A)垂直(B)两条直线
(C)同一条直线(D)两条直线垂直于同一条直线
5.已知△ABC的三个内角度数比为2:3:4,则这个三角形是().
(A)锐角三角形(B)直角三角形
(C)钝角三角形(D)等腰三角形
6.若三角形的三个外角的度数之比为2:3:4,则与之对应的三个内角的度数之比为().
(A)4:3:2(B)3:2:4(C)5:3:1(D)3:1:
57.若等腰三角形的一个外角为110°,则它的底角为().
(A)55°(B)70°(C)55°或70°(D)以上答案都不对
二、填空题
8.如图,∠A+∠D=180°(已知),∴______∥_______().
∴∠1=_________().
∵∠1=65°(已知),∴∠C=65°().
9.“两直线平行,同位角互补”是______命题(填“真”或“假”).
10•.•把命题“等角的补有相等”改写成“如果„„那么„„”的形式是结果_________,那么__________.
11.命题“直角都相等”的题设是________,结论是____________.
12.在△ABC中,∠B=45°,∠C=72°,那么与∠A相邻的一个外角等于______.
13.在△ABC中,∠A+∠B=110°,∠C=2∠A,则∠A=________,∠B=_______.
14.在直角三角形中,两个锐角的差为20°,则两个锐角的度数分别为_____.
三、解答题
15.判断下列命题的真假,若是假命题,举出反例.
(1)若两个角不是对顶角,则这两个角不相等;
(2)若a+b=0,则ab=0;
(3)若ab=0,则a+b=0.
16.用“如果„„那么„„”改写命题.
(1)有三个角是直角的四边形是矩形;
(2)同角的补角相等;
(3)两个无理数的积仍是无理数.
17.如图,BC⊥ED,垂足为O,∠A=27°,∠D=20°,求∠ACB与∠B的度数.
18.已知:如图,AD ∥BC,BD平分∠ABC。求证:△ABD是等腰三角形
第二篇:八年级数学命题与证明测试题2
3eud教育网 http://百万教学资源,完全免费,无须注册,天天更新!
第二十四章 证明与命题
(一)复习
一、教学目标:
1、了解定义、命题、定理的含义,会区分命题的条件(题设)和结论。
2、会在简单情况下判断一个命题的真假。理解反例的作用,知道利用反例可证明一个命题是错误的。
3、了解证明的含义,理解证明的必要性,体会证明的过程要步步有据。
4、会根据一些基本事实证明简单命题。
2、说明一个命题是假命题,通常只用找出一个反例,但要说明一个命题是真命题,就必须用推理的方法,而不能光凭一个例子。
(二)说一说
1.指出下列句子,哪些是命题,哪些不是命题?
(1)有两个角和夹边对应相等的三角形是全等的三角形;
(2)有两条边对应相等的两个三角形全等;
3eud教育网 http://教学资源集散地。可能是最大的免费教育资源网!
3eud教育网 http://百万教学资源,完全免费,无须注册,天天更新!
(3)作∠A的平分线;
(4)若a=b 则a2= b
2(5)同位角相等吗?
2.说出一个已学过定理:
说出一个已学过公理:
3、下列把命题改写成“如果„„,那么„„”的形式。并判断下列命题的真假.(1)不相等的角不可能是对顶角.(2)垂直于同一条直线的两直线平行;
(3)两个无理数的乘积一定是无理数.(三)练一练
1.用反例证明下列命题是假命题:
(1)若x(5-x)=0,则x=0;
(2)
(3)
(4)若x≠2,(四)例题分析
例1求证:(1)根据题意(2)知”和“求证”;
;
(4);
例2已知:如图,△ABC中,∠C=2∠B,∠BAD=∠DAC.求证:AB=AC+CD
还有其他方法吗?
3eud教育网 http://教学资源集散地。可能是最大的免费教育资源网!
3eud教育网 http://百万教学资源,完全免费,无须注册,天天更新!
A
BDCBDC
(第三题)(第二题)
例3已知 :如图D,E分别是BC,AB上的一点,BC、BD的长度之比为的面积是△ABC的面积的一半.求证: BE=3AE
例
4、已知:如图,直线AB,CD,EF在同一平面内,且 EF∥ EF,求证:AB ∥ CD。
证明:假设AB∥CD,那么AB与CD∵AB ∥ EF,CD ∥ EF(已知)
∴过点P有两条直线AB,CD都与直线∴AB ∥ CD不能成立。
∴AB ∥ CD
&科&
1.;
2.3.写出结论(肯定原命题成立)。
练习:
如图,已知:AB=AE,BC=DE,∠B= ∠E,AF⊥CD于F.求证:CF=DF.(五)小结:
(六)作业布置:练习一份
3eud教育网 http://教学资源集散地。可能是最大的免费教育资源网!
3eud教育网 http://百万教学资源,完全免费,无须注册,天天更新!
3eud教育网 http://教学资源集散地。可能是最大的免费教育资源网!
第三篇:八年级下复习测试题 Unit 7-8
Revision test for Unit7-8
一.根据含义和首字母完成单词。
1.It’s i_______ to talk loudly in the reading room.2.I hope you don’t m_______ opening the door.3.Last night your mother _________(抱怨)about to me about your poor marks in the test.4.My father got a________ when he found I don’t do my homework again.5.Must we find a good_________(解决办法)now?
6.What’s the best gift you have ever _________(收到)?
7.What should I g______ my father on Father’s Day?
8.Teachers often ________(鼓励)and help us to study well.9.You should follow your doctor’s s_______.10.He went there i_____ of me.11.Could you please take out the trash? Ok.I’ll do it right a____
12.I’ll make a _________(特别)meal for my parents tomorrow.13.The ticket to the match c_____ me 20yuan.14.Would you mind t_______ down the radio?
15.Flowers are not creative e_________.二.用所给词的适当形式填空。
1.Why don’t ______(go)camping with them?
2.How about _________(hike)this weekend?Why not ______(keep)down your voice? Here is the library.The man was too _______(tire)_________(walk).5.Could you please ________(feed)my cat?
6.The bike is___________(expensive).I will take it.7.Tomorrow is my sister’s______(nine)birthday.8.Making a lot of money made her more_________(interest)in_______(do)business.9.The teacher is coming.Would you mind ________(clean)the blackboard?
10.I have some difficulties ________(finish)the work in two days.11.It’s impolite to ask________(person)questions.12.He always encourages me___________(improve)my speaking skill..13.It’s enough ___________(make)your grand mother happy.14.He has a daughter _______(name)Lily.15.Let’s go swimming instead of _______(go)for a walk.三.单选。
()1.Would you like to come to my birthday party? —Yes, ____________ I’m very busy.A.I like to, andB.I’d like to, butC.I would like, and
()2.—Would you please ______ football near my home?— ____________.A.not to play, NoB.not play, Yes, I will do that again
C.not play, Sorry, I won’t do that againD.don’t play, Sorry, I won’t do that again
()3.I’ll do it _____ a minute.A.atB.onC.inD.after
()4.______ dolls to children at McDonald’s isn’t good.A.SellingB.SellC.SellsD.To sellin
()5.Try ______ late for school again.A.not to beB.not beC.to be not
()6.Get up early, ______ you ______ late for school.A.and, will beB.or, will beC.or , areD.so, are
()7.When you are ______, you can come to me for help.A.in troubleB.troubleC.in dangerousD.in matter
()8.—Would you mind moving your bike a little to make room for mine? —______.A.Yes, I wouldB.OK, I’ll do it right nowC.Wait a moment
()9.— Where are you going? —I’m going shopping.—___________?—Certainly.A.Will you give me penB.Could you get a pen for me
C.Can I help youD.What are you going to buy
()10.John is much better than I________.A.to playing chessB.for playing chessC.at playing chessD.in playing chess
()11.He has ___________ daughter_______ Mary.A.a eight years old , nameB.an eight-years-old , named
C.an eight-year-old , namedD.a eight-year-old , naming
()12.The classroom is very dirty today.It is hard _______.A.cleaningB.to clean itC.to cleaningD.to clean
()13.I don’t think you are right.So I can’t ________ you.A.agree withB.agree toC.agree onD.agree
()14.Mum’s birthday is coming.What about _______ her some flowers?
A.getB.gettingC.to getD.got
()15.He was very excited about _______a picnic.A.havingB.to haveC.haveD.to having
四.句型转换。
1.I would like to have some bananas.(一般疑问句)
_____________ you _______________ to have some bananas?
2.Would you mind not playing baseball here?(同义句)
Could you ________________ not ________________ baseball here?
3.The boy is too heavy to run fast.(改同义句)The boy is ___ heavy that he ____ run fast.4.I have a cat.It’s name is Mimi.(合并成一句)I have a cat_______ Mimi.5.It’s fine weather today.(改感叹句)_____ ______ _______ it is today!
五.完形填空
What is the best way to study? This is a very important question.Some Chinese students
oftenvery hard for long hours.This is ahabit, but it is not a better way to study.An
efficient student mustenough sleep, enough food and enough rest.Every week youto
go out for a walk or visit some friends or some nice places.It's goodyour study.When you
return to your studies, you'll find yourselfthan before and you'll learn more.Maybe we canthat learning English istaking Chinese medicine.We don't mean that
it's bitter.We mean that like Chinese medicine, the effi cient of your studyslowly but
surely.slowly but surely every day and effects will come just like Chinese medicine.()1.A.playB.studyC.sleepD.think
()2.A.bestB.betterC.goodD.bad
()3.A.haveB.doC.wantD.make
()4.A.wantB.hopeC.needD.wish
()5.A.inB.forC.toD.at
()6.A.weakerB.strongerC.fatterD.thinner
()7.A.sayB.guessC.talkD.know
()8.A.aboutB.onC.asD.like
()9.A.returnsB.comesC.givesD.gets
()10.A.SleepB.KnowC.LearnD.Play
六.阅读理解。
A
Mother’s Day is an important day.It’s a day when children can show their mothers how much
they love them.Many children give flowers to their mothers.This makes them very happy.Most
of the people who live near Mrs Taylor’s flower store are poor.The children don’t have money to
buy flowers.Mrs Taylor helps them.The children work one hour for Mrs Taylor.They can clean
the windows, sweep the sidewalk, and mop the floor in the store.Then Mrs Taylor gives each of
them flowers to take home for their mothers.The mothers who live near Mrs Taylor’s store all
have a wonderful Mother’s Day.判断正(T)误(F)
()1.Many children make their mothers happy by giving flowers to them.()2.When the children work for Mrs Taylor,they grow flowers.()3.The children in the story often buy flowers for their mothers.()4.You can tell that Mrs Taylor is a kind-hearted woman.()5.The story is about Mrs Taylor’s birthday.B
I’m taking my family to other countries to have a trip.My wife and I and our two children
are all going along.My elder brother will go with us, too.He has never been overseas and he is
even more excited than the children.My father is so old that he’d like to stay at home and take
care of the house.We’re going by train to New York, and then take a ship to Europe.When we arrive in
Europe, we’re going to some countries for sightseeing(观光).We’ll go to places either by train or
by bus.We’re going to fly home.It took us a long time to decide where to go, but I think we’ll have a very interesting trip.We’ll go to England, France and Italy.We also talked about how we would go to Europe.At first
we wanted to fly because it would be faster and would save more time, But my brother likes to
take a boat trip and the children like that, too.()1.How many people of the family will go to have a trip?
A.ThreeB.FourC.FiveD.Six
()2.My father will not go on the trip because ____.A.he doesn’t like travelsB.staying at home is more interesting
C.he is too old to travelD.nobody wants to take him along
()3.We’re coming back home by_____.A.seaB.airC.busD.train
()4.In Europe we will _____.A.go sight-seeing at the seasideB.to go to different countries by ship
C.buy a lot of presentsD.go from place to place by train or by bus
()5.My brother and my children would like to _____.A.do some shopping in EuropeB.study the Italian language in Italy
C.enjoy a trip by shipD.learn French in France
七.补全对话。
A: It’s Nick’s birthday next Sunday.What ____ I get him?
B: What’s the best gift he ___ ever received?A: A bike.B: _________ did he get it?A: _________ his tenth birthday.B: Who ________ it to him?A: His parents.B: What a _______ guy!I think you should get him _________ special.What about a
p__________? It can learn to speak like a man!
A: No, I’m afraid not.Because his mother doesn’t want him to ________ a pet.I think I’m
_________ to buy a big birthday cake.B: Not bad.八.仔细阅读下面的文章,用所给动词的适当形式填空。
Yesterday afternoon two thieves wearing police uniform arriving at the museum and ask the
guard(1)______(show)them Monet’s paintings.They said that they had received a telephone call
at the police station that morning telling them that the paintings were in danger.The guard
immediately let them(2)_____(see)the paintings.The thieves told them(3)_______(turn off)the
alarm system and then suddenly they made him(4)____(lie)on the ground and they tied his arm
and legs.They worked very quickly and carefully and when they had collected the best paintings
they(5)_____(leave)the museum quietly and calmly through the front door.(1)________(2)_________(3)________(4)__________(5)___________
第四篇:初中数学命题与证明
命题与证明
一、选择题
1、(2012年上海黄浦二模)下列命题中,假命题是()
A.一组邻边相等的平行四边形是菱形;
B.一组邻边相等的矩形是正方形;
C.一组对边相等且有一个角是直角的四边形是矩形;
D.一组对边平行且另一组对边不平行的四边形是梯形.答案:C2、(2012温州市泰顺九校模拟)下列命题,正确的是()
A.如果|a|=|b|,那么a=b
B.等腰梯形的对角线互相垂直
C.顺次连结四边形各边中点所得到的四边形是平行四边形
D.相等的圆周角所对的弧相等
答案:C
3(2012年中考数学新编及改编题试卷)下列语句中,属于命题的是()..
(A)作线段的垂直平分线(B)等角的补角相等吗
(C)平行四边形是轴对称图形(D)用三条线段去拼成一个三角形
答案:C4、(2012年上海市黄浦二模)下列命题中,假命题是(▲)
A.一组邻边相等的平行四边形是菱形;
B.一组邻边相等的矩形是正方形;
C.一组对边相等且有一个角是直角的四边形是矩形;
D.一组对边平行且另一组对边不平行的四边形是梯形.答案:C5、(2012年上海金山区中考模拟)在下列命题中,真命题是……………………………………………………………………………………………()
(A)两条对角线相等的四边形是矩形
(B)两条对角线互相垂直的四边形是菱形
(C)两条对角线互相平分的四边形是平行四边形
(D)两条对角线互相垂直且相等的四边形是正方形
答案:C
二、填空题
1、三、解答题
1.(2012年江苏海安县质量与反馈)已知:如图,在△ABC中,BC=AC,以BC为直径的⊙O与边AB相交于点D,DE⊥AC,垂足为点E.
⑴求证:点D是AB的中点;
⑵证明DE是⊙O的切线.
答案:22.(1)略;(2)略.
2.(2012年江苏通州兴仁中学一模)如图,在□ABCD中,E为BC的中点,连接DE.延长DE交AB的延长线于点F.求证:AB=BF.
E C
答案:由□ABCD得AB∥CD,∴∠CDF=∠F,∠CBF=∠C.
又∵E为BC的中点,∴△DEC≌△FEB.
∴DC=FB.
由□ABCD得AB=CD,∵DC=FB,AB=CD,∴AB=BF.
3、(盐城地区2011~2012学适应性训练)(本题满分10分)如图,AB是⊙O的直径,点A、C、D在⊙O上,过D作PF∥AC交⊙O于F、交AB于E,且∠BPF=∠ADC.(1)判断直线BP和⊙O的位置关系,并说明你的理由;
(2)当⊙O5,AC=2,BE=1时,求BP的长.(1)直线BP和⊙O相切.……1分
理由:连接BC,∵AB是⊙O直径,∴∠ACB=90°.……2分
∵PF∥AC,∴BC⊥PF, 则∠PBH+∠BPF=90°.……3分
P
∵∠BPF=∠ADC,∠ADC=∠ABC,得AB⊥BP,……4分
所以直线BP和⊙O相切.……5分
(2)由已知,得∠ACB=90°,∵AC=2,AB=25,∴BC=4.……6分
∵∠BPF=∠ADC,∠ADC=∠ABC,∴∠BPF=∠ABC,由(1),得∠ABP=∠ACB=90°,∴△ACB∽△EBP,……8分
∴ACBC解得BP=2.即BP的长为2.……10分 BEBP
4.(盐城市第一初级中学2011~2012学年期中考试)(本题满分10分)如图,在△ABC中,∠B=60°,⊙O是△ABC外接圆,过点A作⊙O的切线,交CO的延长线于P点,CP交⊙O于D;
(1)求证:AP=AC;
(2)若AC=3,求PC的长.
答案(1)证明过程略;(5分)
(2)3
35(徐州市2012年模拟)(6分)如图,在平行四边形ABCD中,E,F为BC上两点,且BECF,AFDE.
求证:(1)△ABF≌△DCE;
(2)四边形ABCD是矩形. A D
B C E F
(第21题)答案:解:(1)BECF,BFBEEF,CECFEF,······························· 1分 BFCE.
四边形ABCD是平行四边形,ABDC. ······························ 2分 在△ABF和△DCE中,ABDC,BFCE,AFDE,△ABF≌△DCE. ··························· 3分
△ABF≌△DCE,(2)解法一:
BC. ······························ 4分 四边形ABCD是平行四边形,AB∥CD.
BC180.
BC90. ···························· 5分
·························· 6分 四边形ABCD是矩形.
解法二:连接AC,DB.
△ABF≌△DCE,AFBDEC.
AFCDEB. ··························· 4分 在△AFC和△DEB中,AFDE,AFCDEB,CFBE,△AFC≌△DEB.
ACDB. ······························ 5分 四边形ABCD是平行四边形,·························· 6分 四边形ABCD是矩形.
6.(盐城地区2011~2012学适应性训练)(本题满分12分)如图,△AEF中,∠
EAF=45°,AG⊥EF于点G,现将△AEG沿AE折叠得到△AEB,将△AFG沿AF折叠得到△AFD,延长BE和DF相交于点C.
(1)求证:四边形ABCD是正方形;
(2)连接BD分别交AE、AF于点M、N,将△ABM绕点A逆时针旋转,使AB与AD重合,得到△ADH,试判断线段MN、ND、DH之间的数量关系,并说明理由.(3)若EG=4,GF=6,BM2,求AG、MN的长.
AHBENFDC(1)由∠BAD=∠ABC=∠ADC=90°,得矩形ABCD,……2分
由AB=AD,得四边形ABCD是正方形.……3分
222(2)MN=ND+DH.……4分
理由:连接NH,由△ABM≌△ADH,得AM=AH,BM=DH,∠ADH=∠ABD=45°, ∴∠NDH=90°,……6分
再证△AMN≌△AHN,得MN=NH,……7分
222∴MN=ND+DH.……8分
(3)设AG=x,则EC=x-4,CF=x-6,22由Rt△ECF,得(x-4)+(x-6)=100,x1=12,x2=-2(舍去)∴AG=12.……10分
由AG=AB=AD=12,得BD=122,∴MD=92,222设NH=y,由Rt△NHD,得y=(92-y)2),y=52,即MN=52.……12分
7.(盐城地区2011~2012学适应性训练)(本题满分8分)如图,已知E、F分别是□
ABCD的边BC、AD上的点,且BE=DF.
(1)求证:四边形AECF是平行四边形;
(2)若BC=10,∠BAC=90°,且四边形AECF是菱形,求BE的长.
AFD
BEC
证:(1)由□ABCD,得AD=BC,AD∥BC.……2分
由BE=DF,得AF=CE, ∴AF=CE,AF∥CE.……3分
∴四边形AECF是平行四边形;
(2)由菱形AECF,得AE=EC,∴∠EAC=∠ACE.由∠BAC=90°,得∠BAE=∠B,∴AE=EB.∴BE=AE=EC,BE=5.……4分 ……5分 ……7分 ……8分
第五篇:八年级数学图形的证明测试题
3eud教育网 http://百万教学资源,完全免费,无须注册,天天更新!
第十一章 图形的证明一 测试
一,选择
1.下列关于判断一个数学结论是否正确的叙述正确的是()
A.只需观察得出B.只需依靠经验获得
C.通过亲自实验得出D.必须进行有根据地推理.2.通过观察你能肯定的是()
A.图形中线段是否相等;B.图形中线段是否平行
C.图形中线段是否相交;D.图形中线段是否垂直
3.下列问题你不能肯定的是A.一支铅笔和一瓶矿泉水的体积大小关系;B.三角形的内角和
C.n边形的外角和;D.4.下列问题用到推理的是A.根据x=1,y=1 得x=y;B.;
C.5.下列句子中,是命题的是A.今天的天气好吗AB∥CD;
C.连结A、B两点D.6.A.;B.两互补的角一定是邻补角
C.如果a如果两角是同位角,那么这两角一定相等
7.()
A.如果a∥c,那么a∥c;B.锐角三角形中最大的角一定大于或等于60°
C.两条直线被第三条直线所截,内错角相等;D.矩形的对角线相等且互相平分
8.已知下列四个命题:(1)若直角三角形的两边长分别是3与4,则第三边长是5;(2)
(3)若点P(a,b)在第三象限,则点Q(-a,-b)在第一象限;(4)两边及第三(a)2a;2边上的中线对应相等的两个三角形全等,其中正确的选项是()
A.只有(1)错误,其他正确B.(1)(2)错误,(3)(4)正确
3eud教育网 http://教学资源集散地。可能是最大的免费教育资源网!
3eud教育网 http://百万教学资源,完全免费,无须注册,天天更新!
C.(1)(4)错误,(2)(3)正确D.只有(4)错误,其他正确
二,填空
9.有一正方体,将它各面上分别标出a、b、c、d、e、f。有甲、乙、丙三个同学站在不同角度观察结果如图,问这个正方体各个面上的字母的对面各是什么字母,即a的对面为,b的对面为,c的对面为.10.某参观团依据下列约束条件,从A、B、C、D、E
(1)如果去A地,那么也必须去B地;
(2)D、E两地至少去一处;
(3)B、C两地只去一处;
(4)C、D两地都去或都不去;
(5)如果去E地,那么A、D1
1条件是:,结论是:___________________.
12.如图,Rt△°,AD平分∠BAC,BD平分∠CBE,则∠ADB=______°.
13.∠
1、∠
2、∠3分别是△ABC的3个外角,则∠1+∠2+∠3=_______°.
14.下面的句子中是命题的有___________________.
(1)我是扬州人;(2)你吃饭了吗?(3)对顶角相等;(4)内错角相等;
(5)延长线段AB;(6)明天可能下雨;(7)若a>b则a>b.三,解答
15.判断下列命题的真假:(1)同角的余角相等;(2)异号两数相加得零;
23eud教育网 http://百万教学资源,完全免费,无须注册,天天更新!
(3)等腰梯形是轴对称图形;(4)鸦片战争是中国近代史的开端;
(5)平行于同一条直线的两直线平行;
(6)函数yx1的自变量x的取值范围是x1;
(7)在三角形中,两边之和小于第三边。判断其中的真命题与假命题
16.下面的判断是否正确,为什么?
(1)对于所有的自然数n,n的末位数都不是2.(2)当n=0,1,2,3,4,5时,n+n的值是偶数吗?你能否得到结论:n,n+n的值都是偶数.17
(1)能被2整除的数也能被4(2(3)若xy=0,(418.请把下面证明过程补充完整:
已知:如图,DE∥BC,BE平分∠ABC.求证:∠1=∠3.
证明:因为BE平分∠ABC(已知),所以∠1=______(). 222
3eud教育网 http://百万教学资源,完全免费,无须注册,天天更新!
又因为DE∥BC(已知),所以∠2=_____().
所以∠1=∠3().
19.地理老师在黑板上画了一幅世界五大洲的图形,并给每个洲都写上了代号,然后,他请5个同学每人认出2个大洲来,5个同学的回答是:
甲:3号是欧洲,2号是美洲;
乙:4号是亚洲,2号是大洋洲;
丙:1号是亚洲,5号是非洲;
丁:4号码是非洲,3号是大洋洲;
戊:2号码是欧洲,5号是美洲;
地理老师说:“你们每个人都认对了一半”
边对应成比例。
已知:如图,△ABC中,分析:要证BDAB、AB与DC、AC所在的三
DCAC
ABD与△ADC不相似,需要考虑用别的方法换比。
AC恰是BD、DC、AB的第四比例项,所以考虑过C作CE∥AD,BDAB交BD、DC、AB的第四比例项AE,这样,证明就可DCAC(1BA的延长
下证明过程)
∴AE=AC()线于E。
(完成以
3eud教育网 http://百万教学资源,完全免费,无须注册,天天更新!
∴△BAD~△BEC∴
∴BDAB()BCBEBDAB DCAC
(2)用三角形内角平分线性质定理解答问题:
已知:如图,△ABC中,AD是角平分线,AB=5cm,AC=4em,BC=7cm。求:BD的长。A
D