平行线的性质专项练习60题有答案okWord文档下载推荐.docx
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/1=30
25.如图所示.CD是ZACB勺平分线,/ACB=40°
/B=70°
DE//BC和宏ZBDCD度数.
26.如图,点A在直线MN上,且MN//BC,求证:
/BAC+/B+/C=180
27.已知:
如图,OP平分ZAOB,MNIIOB.求证:
/1=/3.
28
29.已知,如图,
AD//BC,Z1=/2,ZA=12!
D上CD求ZC的度数.
30.如图,已知直线AB//CD,直线m与AB、CD相交于点E、F,EG平分ZFEB,ZEFG=50°
求新度数EG
BOD,ZD=52。
,求Z的>OE
/ABF=25°
求剧度魏CE
/D=/C,求ZD的度纶ZB
A=105°
/ACE=51的度IBZE
35.如图:
a//b,Z1=122
/3=50和£
饷度数.
36.如图,已知AB//CD,Z1=50°
BD平分ZADC,求Z甫勺度数.
38.如图,若ABIIEF,ZC=90°
x+y-z度数.
PAG数
41.如图,已知DB//FG//EC,ZABD=84°
/ACE=60是£
BAC勺平分线.求Z
42.已知:
如图AB//CD,Z1=/A,Z2=zB、CE、D在一条直线上.
求ZAEC勺度数.
43.已知:
如图,直线liII2,ABX1垂足为O,BC与12相交于点D,Z1=43°
求度数.
MN,分别交直线EF于点C、D,ZBCD、ZCDN角平分线交于点G,>
CG乾度数.
44.如图,直线AB//
BEC,EG±
EF.求Z和BEGDEG.
45.如图所示.已知AB//CD,ZB=100EF平分Z
46.如图AE//BD,ZCBD=57°
/AEF=125°
,的蛾数,并说明理由.
47.已知:
如图,△
tAB俄D在AC的延长线上,CE是ZDCB勺角平分线,且CE//AB.
E
求证:
ZA=/B.
48.如图,/ABDBDC勺平分线相交于点E,BE交CD于F,Z1+/2=90。
,试问:
直AB、CD在位置上有
什么关系?
Z2与Z3在数量上有什么关系?
49.如图,已知直线AB//CD,直线GH分别与直线AB、CD交于点E、G,直线CF交直线GH于点F,已知ZCFG=30
/HEB=50。
,求ZFCG^.
50.如图,AB//CD,BC//ED,求:
/B+O).
51.如图,已知AB//CD,ZB=/DCE,求证CD平分ZBCE.
52.如图,已知AB//CD,ZB=40CN是ZBCE勺平分线,CMLCN,求ZBCM数.
53
AE=BE.
55.如图,CD±
AB,DE//AC,EF±
AF平分ZBED,求证:
CD平分ZACB.
BEC
56.如图,△ABCEB平分ZABCEC平分△ABC外角ZACG,过止作DF//BC^AB于D,交AC于F,
DB-CF=DF.
BCG
57.已知:
如图所示,AB//EFDf分ZGFDGF交AB于M,ZGMA=52°
求ZB畛.
58.如图,/BAP+ZAPD=180°
/1=/2,求证:
/E=ZF.
59.如图,已知DE//AB,DF//AC,ZEDF=85°
ZBDF=63
(1)ZA的度数;
(2)ZA+/B+Z的度数.
60.如图,已知AB//CD,Z1=/2,ZEFD=56°
求新度数GD
平行线的性质60题参考答案:
1.AB//CD,
•••ZA=/PED两直线平行,同位角相等)
又ZPEI^APC的外角,
..ZP+ZC=ZA.
2.解法一:
过C点作CF//AB,
则Z1=/ACF=35°
(两直线平行,内错角相等),
•.•ZP+匕C=匕PED,
AB//ED,CF//AB(已知)
•••CF//ED(平行于同一直线的两直线平行)
又..A评分ZCAE,
..ZFCD=1802=180°
-80°
=100(两直线平行,CAD=/DAE,
同旁内角内角互补)
..ZACD=/ACF+/FCD=35°
+100°
=135°
解法二:
延长DC交AB于F
AB//ED(已知)
•••ZBFC=/2=80。
(两直线平行,内错角相等,)
•••/ACF=/BFC-Z1=80°
-35°
=45°
(三角形一个外角等于它不相邻的两个内角的和)
..ZACD=180°
-ZACF=180°
-451=135
=180°
)
解法三:
延长AC、ED交于F
.•AB//ED,DFC=/1=35°
.ZCDF=180°
-Z2=180-80°
=100°
•.•ZACD=ZCDF+ZDFC=100°
+35°
即ZC=/B.
4.AD//EF(已知)
•••ZBAD=/E(两直线平行,同位角相等)
/DAC=/F(两直线平行,内错角相等)
•••/E=/F(已知)
•••ZBAD=ZDAC(等量代换)
•••AD是ZBAC勺平分线.
(5.设Z3=3x,/2=2x,
由Z3+/2=180°
W+2x=180°
x=36,
•••Z2=2x=72;
.•AB//CD,
•.•Z1=/2=72°
6..•AB//CD,
BEF+ZEFD=180°
.•E芽分ZBEFFG平分ZDFE,
在^efG3,
/G=180°
-Z1-Z2=90
EG±
•.•ZC=ZCAD,ZB=ZDAE,
10
J
G
F
i
c-
9..•AD//BC,•••ZEAD=/B=25ZDAC=ZC=30°
.AB//CD,
•••ZACD=180-65°
=115°
.•AC±
BC,
•••ZBCD=115-90°
=25°
.
11.过点E作EF//AB,
AEF=ZBAE=45°
•••EF//CD,
..ZFEC=/DCE=45°
AEC=ZAEF+ZFEC=90°
AE±
CE.
I土■
匚
CD
12.AB//CD,ZABC=55°
•••ZBCD=/ABC=55°
.•EF//CD,
•••ZECD+/CEF=180°
.ZCEF=150°
•.•ZECD=180°
-ZCEF=180-150°
=30
•••ZBCE=/BCD-ZECD
=55-30°
•••ZBCE度数为25°
13.设Z1为x,
ZEAC=ZEAD+ZDAC=25°
+30°
=55
..Z2=x,
•••ZDBC=/1+/2=2x,
.ZD:
ZDBC=21:
•••ZD=2X2x=4x,
.•DE//BC,
•••ZD+/DBC=180°
即2x+4x=180°
解得x=30°
•••ZDEB=/1=30°
14.EF±
ABE,MN//AB
EF±
MN
即ZEFM=90°
.•MN//CD
•••ZNFH=/GHD=180-130°
=50°
•.•ZEFH=ZEFM+ZNFH=90°
+50°
=140
15.AC//BD,•••Z1=/2.
又.ZA=/D,
/A+/1+/E=180。
,/D+/2+/F=180°
•••ZE=/F.
16...•HG//AB(已知)
1=/3(两直线平行,内错角相等),
又HG//CD(已知)
•••Z2=/4(两直线平行,内错角相等),
AB//CD(已知)
•••ZBEF+ZEFD=180。
(两直线平行,同旁内角互补)
又EW分ZBEF(已知)
BEF(角平分线的定义),
又F漆分ZEFD(已知)
•••Z2=ZEFD(角平分线的定义),
•••Z1+ZS=(ZBEF+ZEFD)
.•./1+Z2=90°
3+/4=90°
(等量代换)
即ZEGF=90°
17.AD//BC,
•••Z2=/1=30°
.•AB±
AC,
..ZB=90-/2=60°
18.过E作EF//AB,
•••AB//EF//CD,
•.•ZB=ZBEF=45°
ZDEF=ZD=20
21.AB//CD,
•.•Z1=ZBEF+ZDEF=45°
+20°
=65
19.OB,OC分别是ZABC,ZACB分线,
•••Z1=/2,/4=/5,.•OE//AB,OF//AC,•••Z1=/3,/4=/6,
BE=OE,OF=FC,
•••BC=BE+EF+FC=OF+OE+EF
•••△O曲周长=10,
BC=10.
20.AB//CD,ZC=60
..ZEFB=ZC=60°
:
.ZEFB=ZA+ZE,
•.•ZA+ZE=60
•••ZC=ZB.
.ZB=55°
.•./C=55°
.•BC//DE,
.•./C+ZD=180°
即ZD=180°
-ZC=180-55°
=125
22.EF//BC,
•••ZEOB=/OBC,ZFOC=/OCB,
.•BO,CO分别平分ZABC,匕ACB,
..ZOBC=/ABC^X50°
22
/OCB』/ACB」X60°
=30°
22
EOB=25°
ZFOC=30°
又.•』EOB+ZBOC+ZFOC=180°
•.•ZBOC=180°
-ZEOB-ZFOC=180
30°
=125°
23.AB//CD,
•••ZB+/BCD=180°
.ZB=120°
•••ZBCD=60°
;
又.•C解分ZBCD,
.•./2=30°
..AB//CD,
25°
-
•.•Z1=Z2=30
.•./B+ZC=180°
•.•ZB=180°
29.AD//BC,
•.•ZABC=180°
-ZA=60°
/ADB=/2,
Z1=/2,
•••Z1=/ADB=/2=30°
.•BD±
CD,
•••ZBDC=90°
ZC=180°
-(30°
+90°
)=60°
故ZC的度数为60°
30...•ABIICD(已知)
•••ZEFG+/FEB=180°
(两直线平行,同旁内角互补)
•••/EFG=50°
(已知)
•../FEB=130°
(等式的性质)
24.AB//CD,
..ZEFB=/C=65°
..ZE=/EFB-ZA=65-40°
25.C斑ZACB勺平分线,ZACB=40
•••ZDCB=/ACD=20°
又DE//BC,
•••ZEDC=/DCB=20°
在^BC映,.•』B=70°
•••/EDCZBDC勺度数分别为20°
、90°
26.MN//BC,
.•./B=ZMAB,ZC=ZNAC,
.ZMAB+ZBAC+ZNAC=180°
•.•ZBAC+ZB+ZC=180°
27.。
呼分ZAOBI已知)
1=/2(角平分线定义)
.•MN//OB(已知)
2=/3(两直线平行,内错角相等)
1=/3(等量代换)
28.AB//CD,
..ZD=/1=55°
•••/C=ZD,
E芽分ZFEB(已知)
•••/FE^ZFEB=65。
(角平分线的定义).
31.CD//AB,
•••ZBOD=/D=52°
.•。
坪分ZBOD,
•••ZBOE=26°
32.如答图所示,
L1IIL2,
•.•ZC=55
•.•ZECB+ZCBF=180
ECA+ZACB+ZCBA+ZABF=180
•.•ZCDB=Z1=50°
ZADC=100
.ZA=90°
•.•ZACB+ZCBA=90
又AB//CD,
•.•ZADC+ZA=180
又ZABF=25
•.•ZA=80
•.•ZECA=180-90°
-25°
=65°
33.ZD=/C=45°
/B=135°
理由:
AB//CD,
•■-ZD=/1=45°
(两直线平行,同位角相等)
37.DE//BC,C=ZAED=72°
.•B坪分ZABC,且ZABC=ZACB,
•••ZEBC=ZABC』X72°
=36°
[22
在^BEC,ZCEB=180-72-36°
=72
•••ZB+/C=180°
•••/D=/C=45°
..ZB=180°
-ZC=180-45°
34.CD//AB,
.•./A+ZACD=180°
又.•CD//EF,
•••ZE=/ECD=/ACD-ZACE=75-51°
=24
35.a//b,Z1=122°
•.•Z2=/5=180°
-Z1=180-122°
=58°
..a//b,Z3=50°
38.如图,过点C、D分别作CM、DN平行于AB、
EF,
则x=/5,4=/3,1=/z,
又Z1+Z3=y,/4+5=90°
即x+/4=90°
又Z4=Z3=y-Z1=y,-
x+y-z=90°
Z3=Z6=50
•.•Z4=50
39.AB//DE,ZB=70
•.•ZDCB=180°
-ZB=180-70°
=110
ZBCE=ZB=70°
.•CM平分ZDCB,
•••ZBCM=ZDCB^X110°
CMLCN,垂足为C,
ZBCN=90
BCM=90
55°
=35
43.解法一:
延长AB交12于点E.ABL1,li//2,
AB±
2.
.Z2是^BE的外角,「•/2=90°
+/1=90°
+43°
=133
•••ZNCE=/BCE-ZBCN=70-35°
40.ZA=/3.理由如下:
.•DE//AB,
•••Z1=/A,Z2=/3,
又1=/2,
•.•ZA=Z3
41.DB//FG//EC,
•••ZBAG=/ABD=84°
/GAC=/ACE=60
•••ZBAC=/BAG+/GAC=144°
•••AP^ZBAC勺平分线,
•••ZPAC=ZBAC=72°
2
•••ZPAG=/PAC-ZGAC=72°
-60°
=12
42.过E作EF平行于AB,贝UEF//CD,
.•AB//EF,
.•./A=ZAEF=Z1,
.•CD//EF,
•••ZC=/FEC=/2,
.ZBED=180°
.•./1+ZAEF+ZFEC+Z2=180°
即
ZAEF+ZCEF=X180=90°
过点B作BF//1,利用平行线的性质求出/2
的度数.
1II2,BF2,1
..ZABF=180°
-90°
=90°
ZFBC=/1=43
..Z2=ZABF+ZFBC=90°
=133°
44.AB//MN(已知)
•../BCD+ZCDN=180°
CG、DG是角平分线
..Z1+Z2=90
•••/1+/2+/CGD=180。
(三角形内角和等任0°
)..ZCGD=90
45.由题意得:
/BEC=80°
/BED=100
ZBEF=-ZBEC=40
=140
•••ZBEG=90-/BEF=50°
/DEG=/BED-50°
•••/BEGZDE副为50°
46..•』AEF=125,
•••ZCEA=55°
.•AE//BD,ZCDB=/CEA=55°
在^BC映,.•』CBD=57°
.•./C=68°
47.C是ZDCB勺角平分线,
•••Z1=/2.
.•CE//AB,
.•./1=ZA,Z2=ZB,
.•./A=ZB.
48.AB//CD,Z2+/3=90°
理由如下:
.•BE、DE分另U平分ZABD、ZCDB,
..ZABD=2/1,ZBDC=2/2.
.Z2+Z1=90°
•••ZABD+/CDB=180°
•••AB//CD.
..Z3=/ABF.
.Z1=/ABF,匕2+/1=90°
•••ZFGD=50°
又.•』CFG=30°
FCG=20°
50.AB//CD,BC//ED,
•••ZB=/C,ZC+/D=180°
.•./B+ZD=180°
51...ABIICD(已知,)
•••ZB=/BCD(两直线平行,内错角相等)
又B=/DCE(已知)
•••ZBCD=/DCE(等量代换)
即CD平分ZBCE.
52.AB//CD,ZB=40°
•.•ZBCE=180°
-ZB=180-40°
CN是ZBC的平分线,
=70
..CMLCN,
ZBCM=20
53.DE//AC,
ADE=ZCAD,
AD是ZBAC勺平分线,
EAD=ZCAD,
•../ADE=/EAD,
AE=DE,
Z2+Z3=90
AD,
ADE+ZBDE=90°
ZE