中考数学复习题方法技巧专题七角平分线训练

方法技巧专题(七) 角平分线训练..........

-B=C=M

BCDMADCADC=MAB

-..

...

eq

\o\ac(△,-) ABCAC=ABC=C=ADBC

DABCAD

EAE

-. .. ..

eq

\o\ac(△,-) ABC

DE

BCABCAE

NACB

AD

M.

BC=

MN

-. .. ..

-

ABCDDCABDAB=ACBCAC=BCABC

ADAC

EF

-. - .+. + ..

-

PAOBMPNAOB.MPN

P

OAOB

MN

PM=PNOM+ON

PMONMN.

-. . . ..

-ABCDBADAE

BC

E

BE=ABCD

EC .

-.

eq

\o\ac(△,-) ABC

OACB=ACB

O

D

AC=BD= .

BC

-.

-

ABCDABC

BE

AD

EBED

EF

DC

F

AB=DF=FCBC= .

-.

-OAB=ACAE

AC=ACBAE

AE.

-.

-

ABCDABDCDBBEDFADBC

EF.BEDF.ABE

BEDF.

-.

-BACABCDABCAD

E.DE=DBBAC=BD=ABC.

-.

-BDABCABBDBC

EFG

EDDG.EBGDABC=C=ED=

H

BD

HG+HC

.

-..

BEABDABC=ABE=EBD=.ADBCBDA=.DE=

BE.BAD=-=BAD=ABE=AE=BE=DEAE=

AD.

ACD

C=

AD=AC

C=×

= AE=

× = .

..

ABCBC=AB+AC=.ABCAE

NBA=BEN

AE.ACBAD

MAC=DCM

ADDE=AB+AC-BC=.MNADEMN=

DE=

.

..

F

FGAD

eq

\o\ac(△,G.)

ABCAFG.

FG=

AG=AF= .BEABCABE=..AEB=-ABE=.AFE=CAB+ABE=..AEB=AFEAE=AF= EG= -.FGADDAB=FGAB.

=

= = +.

..

POAOB

PEO=PFO=AOBEPFMPNAOBMPN=EPFMPE=NPF.

PE=PF

PMEPNFPM=PN

ME=NF

OM+ON=OE+OF

OE+OF

OM+ON

PMEPNFPMON

PEOF

eq

\o\ac(△,EF) PMNPEF

MN

EF.

MN.

...

DAACB=ABOADB=.CDACBBD=AD.ABDAB= = =eq

\o\ac(△,.) ABCBC= = =.. +

EF

BCG.ABCDABCBE

AD

EABE=GBE=

ABEABE=AEB=AB=AE=.

ABE

BE=

=

=

.

BED

EF

DC

FBEG=DEF.

ADBCG=DEFBEG=GBG=BE= .G=DEFEFD=GFCEFD

GFC = =

=

.

CG=xDE=x

AD=+x=BC.BG=BC+CG

=+x+x

x=

-

BC=+x=+

-=

+..

BCBEOCOC

BE

G.BAE=BAC=BOCBAE+ABE=OGB=OCBE

BG=EGAE=OG.

OG=x

CG=

-xBC=OB-OG=BC-CG

-x=-

-x

x=

AE=x=

..ABCDABCDBCADABD=CDB.BEABDDFCDBEBD=

ABDFDB=

CDB.EBD=FDB.BEDF.BCADBEDF.ABE=

BEDF.BEABDABE=ABD=DBE=.

ABCDA=ADB=-ABD=-=.DBE=ADBDE=BE.

BEDF

BEDF..ADBACBAD=CAD.CBD=CADBAD=CBD.BEABCCBE=ABEDBE=CBE+CBD=ABE+BAD.BED=ABE+BADDBE=BEDDE=BD.

CD.BAC=BCBDC=.ADBACBD=BD=CD=BC= = ABC ..

EBGD.EGBDEB=EDGB=GDEBD=EDB.BDABCEBD=DBCEDF=GBF.EFDGFBEFDGFBED=BGBE=ED=DG=GB

EBGD.ED

EMBC

MDNBC

N

EC

BD

H

HG+HC

EBMEMB=EBM=EB=ED= EM=

BE= .DEBCEMBCDNBCE