913平行线的判定专项练习60题有答案okWord文档格式.docx
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请说明理由.
43.如图,已知/仁/2=90°
/3=30°
/4=60°
图中有几对平行线?
说说你的理由.平行线的判定---第7页共16页
46.如图,已知B、
C、D三点在同一条直线上,/B=/1,/2=/E,试说明AD//CE.
47.直线AB、CD与GH交于E、F,EM平分/BEF,FN平分/DFH,/BEF=/DFH,求证:
EM//FN.
BE、CF分别平分/ABC和/BCD,请你说出BE与CF的位置关系,并说出你的
DB与EC的位置关系,并说明理由.
50.如图,在△ABC中,CD丄AB,垂足为D,点E在BC上,EF丄AB,垂足为F.
(1)CD与EF平行吗?
为什么?
51.如图,已知:
HG平分/AHM,MN平分/DMH,且/AHM=/DMH.问:
GH与MN有怎样的位置关系,请说明理由.(请注明每一步的理由)
52.已知:
如图,/C=/1,/2和/D互余,BE丄FD于点G.求证:
53.如图,直线AB,CD被EF所截,/3=/4,/1=/2,EG丄FG.求证:
D
54.已知:
如图,CD是直线,E在直线CD上,/1=130
4B
56.如图,四边形ABCD,/1=30°
/B=60°
AB丄AC,理由,反之则不用说明理由.
57.已知:
如图,求证:
BD//CE.
/A=/F,
58.如图,AD丄BC于点D,证明的理由.
/1=2,/CDG=/B,请你判断EF与BC的位置关系,并加以证明,要求写出每步
59.已知:
如图,
CE平分/ACD,/1=/B,求证:
AB//CE.
/3=/4,可以判定哪两条直线平行?
平行线的判定60题参考答案:
1.•/BE平分/ABC,
•••/1=/3,
•//1=/2,
•••/2=/3,
•••BC//DE
2.•//A=/F(已知),
•-AC//DF(内错角相等,两直线平行),
•-/C=/CEF(两直线平行,内错角相等),
•••/C=/D(已知),
•••/D=/CEF(等量代换),
•••BD//CE(同位角相等,两直线平行).
3.•/AB丄BC(已知),
•••/ABC=90°
(垂直定义);
•••BC丄CD(已知),
•••/BCD=90°
(垂直定义),
•••/ABC=/DCB;
•••/1=/2(已知),
•/ABC-/2=/DCB-/1,
即/FBC=/ECB,
•-BF//CE(内错角相等,两直线平行)
4.•/AB丄BC,
•/3+/4=90°
.
•//2=/3,/1+/2=90°
•••/1=/4,
•••BE//DF.
5.AB平行于ON.
证明:
TOP平分/MON,
•/BOA=/NOA,
•//BOA=/BAO,
•/BAO=/NOA,
•AB//ON
6.•//1=/2,
•DC//AB,
•••/A+/ADC=180
又•••/A=/C,
•••/ADC+/C=180°
•••AE//BC.
7.•/BC是/ABE的平分线,
•••/ABC=/CBE(角平分线定义),
•//ABE=/D+/E=/ABC+/CBE,/D=/E,
•/ABC=/D,
•DE//BC
&
过点E作EF/AB.
•/EF//AB,
•••/A=/AEF;
又•//AEC=/A+/C,
•••/AEC=/AEF+/C;
而/AEC=/AEF+/CEF,
•••/CEF=/C,
•••EF//CD,
•••AB//CD.
9.•/AC//ED,
•••/1=/4;
•••/2=/4;
又•/EB平分/AED,
•/3=/4;
•••AE//BD
10.•//1+/BEF=180°
/1=105°
•••/BEF=75°
•//2=75°
•/BEF=/2,
•AB//CD.
11.•//D=/A,
•ED//AB;
•//B=/BCF,
•••AB//CF;
•••ED//CF.
12.•/AB丄BC,CD丄BC(已知),
•••/ABC=/BCD=90°
(垂直定义);
又•••/1=/2(已知),
•••/ABC-/1=/BCD-/2(等量减等量,差相等)
•/EBC=/FCB,
•••EB//FC(内错角相等,两直线平行)
13.•/BE是/B的平分线,
•/1=/CBE,
•//1=/2,
•••/2=/CBE,
•••DE//BC.
14.AC与DF平行,理由如下:
•/BD//EC,
•/DBC+/C=180°
又/C=/D,
•/DBC+/D=180°
•AC//DF.
15.•/AC丄AE,BD丄BF,
•/1+/3=/2+/4=90°
•••/1=35°
/2=35°
•/3=/4,
•••AE//BF.
16.•/AB//CD,
•••/ABC=/BCD(两直线平行,内错角相等);
■:
/1=/2,
•••/ABC-/1=/BCD-/2,
即/EBC=/BCF,
•••BE//CF(内错角相等,两直线平行).
17.•//BAD=DCB,/仁/3(已知),
•••/BAD-/1=/DCB-/3(等式性质),即/2=/4,
•-AD//BC(内错角相等,两直线平行)
18.DF//AB.
理由:
•/DE//CA,
•••/1=/CAD,
•••AD是三角形ABC的角平分线,
•••/BAD=/CAD,
•••/2=/BAD,
•••DF//AB
19.AB//DF(2分)
•//C=/DAE,(已知)
•••AD//BC,(内错角相等,两直线平行)(2分)
•••/D=/DFC,(两直线平行,内错角相等)
•/B=/D,(已知)
•••/B=/DFC,(2分)
•••AB//DF(同位角相等,两直线平行)
20.CF/BD.理由如下:
•/BD丄BE,
•••/1+/2=90°
•••/1+/C=90°
•/2=/C.
•CF//BD.
21.AB//CD.(1分)
#1,
理由如下:
•//1+/MNC=180°
/MNC=•••/1=135°
(2分)又•••/AMN=/2=45°
(3分)
•••/1+/AMN=180°
(4分)
•••AB//CD
22.•/BF平分/ABD,DG平分/CDE,
•••/1=g/ABD,/2吕/CDE,
又•••/ABD=/CDE,
•/1=/2,
•-BF//DG(同位角相等,两直线平行).
23.ED//BF;
证明如下:
•••四边形ABCD中,/A=/C=90°
•••/ADC+/ABC=180°
•/BF、DE分别平分/ABC、/ADC,
•/ADC+/ABC=2/ADE+2/ABF=180°
•/ADE+/ABF=90°
又•••/A=90°
/ADE+/AED=90°
•••/AED=/ABF,
•••ED//BF(同位角相等,两直线平行).
24.在△ECD中
•••/C+/CED+/CDE=180°
(三角形内角和定理)又•//CAB=/CED+/CDE(已知),
•••/C+/CAB=180°
(等量代换),
•AB//CD(同旁内角互补,两直线平行)
25.•/CD丄AB,GF丄AB,
•CD//FG,
•/2=/DCG;
又•//1=/2,
•••/DCG=/1,
•••DE//BC
26.•//CAD=/ACB,
•••AD//BC,
•/EF丄CD,
•/EFC=90°
•//D=90°
•/EFC=/D,
•AD//EF,
•BC//EF,
•••/AEB=/B.
27.•//E=/F,
•••AE//FP,
•••/PAE=/APF;
又•••/BAP+/APD=180°
•AB//CD,
•/BAP=/APC,即/2+/PAE=/1+/APF;
•••/2=/128.•/DC丄EC,
•/1+/2=90°
又/D=/1,/E=/2,
•••/D+/1+/E+/2=180°
根据三角形的内角和定理,得
/A+/B=180°
•••AD//BE
29.•//A+/ABC+/C+/CDA=360°
而/A=/C,BE平分/ABC,DF平分/CDA
•2/A+2/ABE+2/ADF=360°
即/A+/ABE+/ADF=180°
又/A+/ABE+/AEB=180°
•/AEB=/ADF
•BE//DF
30./C=/D.理由如下:
•//A=/F,
•••DF//AC,
AB//CD、
•//1=/DGF,
又•//1=/2,
•/2=/DGF
•DB/EC
•/DBA=/C
•/C=/D
31.•••四边形ABCD中,/A=/C=90°
•/ABC+/CDA=180°
•//1=/2,/3=/4,
•/2+/3=90°
•//A=90°
•/1+/AEB=90°
•/AEB=/3
•BE/FD.
32.•//仁/2,/2=/3,•••/1=/3,
•a/b.
33.CF/OD.
•/DE丄AO,BO丄AO,
•DE/BO,
•/3=/2,
•/1=/3,
•CF/OD
34.•//DOB是^COD的外角,
•/C+/CDO=/DOB,又•••/DOB=/1+/2,而/1=/2,/C=/CDO,
•/2=/C,
•CD/OP
35.
(1)•/DE平分/BDF,AF平分/BAC,
•/BDF=2/1,/BAC=2/2,又•//1=/2,
•/BDF=/BAC,
•DF/AC;
(2)•/AF平分/BAC,
•/BAF=/2.
又•••/1=/2,
•/1=/BAF,
•DE/AF.
36.DE/AB,
•/AD平分/BAC,
•/BAC=2/1,
•/EF平分/DEC,
•/DEC=2/2,
•/BAC=/DEC,
37.•//BDE+/CDE=/A+/ACD,又DE是/BDC的平分线,/ACD=/A,
•/A=/BDE,
•DE/AC.
38./2与/B相等时,AC//BD.理由如下:
•//A=/1,/1=/2,
•/A=/2,
•//2=/B,
•/A=/B,
•AC/BD.
39.MN与EF平行.理由如下:
•//1=/A,
•MN/AB,
•EF/AB,
•MN/EF.
40.•//1+/2=180°
/1+/4=180°
•/2=/4,
•AB/CD.
41.•//E=/F,
•BE/CF
•/EBC=/BCF
•/CBA=/DCB
42.•/EF丄CD于F,
•/EFG=90°
•••/GEF=25°
•/EGF=65°
•//1=65°
•/1=/EGF
43.图中共有2对平行线.
1AB//CD.理由如下:
•//1=/2=90°
•AB/CD(在同一平面内如果两条直线同时垂直于同一条直线那么这两条直线平行);
2•//2=90°
•/4+/5=90°
又•••/3=30°
•/3=/5
•••EF//HG(同位角相等,两直线平行).综上所述图中共有2对平行线它们是:
EF/HG
44.AB/CD
•//1=/2,/1=/3,
•/2=/3
•
义),
而/AHM=/DMH(已知)
•••/GHM=/NMH(等量代换),
■-GH//MN.(内错角相等,两直线平行)
52.•/BE丄FD,
•••/EGD=90°
•••/1+/D=90°
又/2和/D互余,即/2+/D=90°
•••/1=/2,
又已知/C=/1,
•/C=/2,
•AB//CD
53.•/EG丄FG,
•/G=90°
•/1+/3=90°
•//1=/2,/3=/4,
•••/1+/2+/3+/4=180°
54.:
•//1+/2=180°
/1=130°
•••/2=50°
•••/A=50°
•••/A=/2,
55.
(1)•/DE丄AC,BF丄AC,
•/AED=/CFB=90°
•••/DAE+/1=90°
/BCF+/2=90°
•••/DAE=/BCF,
•••AD//BC;
(2)AB//CD.
•//DAE=/BCF,/DAB=/DCB,
•••/DAB-/DAE=/DCB-/BCF,即/CAB=/ACD,
56.
(1)AD与BC一定平行.理由如下:
•/AB丄AC,
•/BAC=90°
•//1=30°
/B=60°
•••/1+/BAC+/B=180°
即/BAD+/B=180°
•••AD//BC.
(2)AB与CD不一定平行.
57.•//A=/F,
•AC//DF,
•••/C=/FEC,
•••/C=/D,
•/D=/FEC,
•BD//CE.
58.EF与BC的位置关系是垂直关系.证明:
•//CDG=/B(已知),
•••DG//AB(同位角相等,两直线平行),•••/1=/DAB(两直线平行,内错角相等),平行线的判定---第15页共16页
•//1=/B,
•••/2=/B,
•••AB//CE.
60.•//1=/2,
•AB/CD,
•//3=/4,
•AD/BC,
故可以判定AB/CD,AD/BC.
又/1=2(已知),
•EF/AD(内错角相等,两直线平行),
•••/EFB=/ADB(两直线平行,同位角相等)又AD丄BC于点D(已知),
•••/ADB=90°
•••/EFB=/ADB=90°
所以EF与BC的位置关系是垂直.
59.•/CE平分/ACD,
•••/1=/2,