4. 如图所示,已知OE平分AOB,BC,OA于C,AD,OB于D.求证.

1.∠EOF=(360-90)/2=135度2.设∠AOC/2=a,∠BOC/2=b=30度∴2×a+(a+30度)=210度∴a=60度∴∠EOF=a+b=60+30=90度

AOB共线那∠AOB是180°了?能上个图吗我马上就能给你解决了!再问：图已给，请写全些再答：∠EOF=∠COE+∠COD+∠DOF=1/2∠AOC+∠COD+1/2∠DOB=1/2(∠AOC+∠DO

∵OE平分∠AOC∴∠AOC=2∠COE=2（∠COF+∠EOF）∵∠BOC=60°,OF平分∠BOC∴∠COF=30°∴∠AOC+∠EOF=2（∠COF+∠EOF）+∠EOF=210°∴∠EOF=5

1：由AO⊥BO和∠BOC=60度可知道∠AOC=150度OE平分∠AOC那么∠COE=75度∠BOE=15度OF平分∠BOC那么∠BOF=30度∠EOF=45度啦2：设∠BOE=x则∠EOF=30度

∵OE平分∠BOD∴∠BOD=2∠BOE,∠DOE=∠BOD／2﹙角平分线定义﹚∴∠AOD:∠BOD=∠AOD:﹙2∠BOE﹚=7:2∵∠AOD＋∠BOD=180º﹙平角定义﹚∴∠BOD=1

图片传不了你至少把∠2、∠1用字母表示吧⊙﹏⊙b汗再问：。。。再答：　　 

OE与OB一定相互垂直∵直线AB,CD相交于点O,∠AOC=28度∴∠BOD=∠AOC=28度（对顶角相等）又∵OE平分∠DOE,∠EOF=31度∴∠EOF=∠FOD=31度∵∠EOF+∠FOD+∠D

我帮你把图片传上去了,你看看我画的对不对 证明：由题意可知,∠AOC与∠COB互补,射线OE又是∠AOC的平分线,射线OF又是∠BOC的平分线,即∠EOF与=90°,射线CF垂直射线于OF,

(1)∵AB=AC,∠BAD=∠CAE,AD=AE,∴△ABD≌△ACE,∴∠B=∠C,又∵∠BOE=∠COD,BE=AB-AE=AC-AD=CD,∴△BOE≌△COD,∴OD=OE(2)∵△ABD≌

(1)∵AB=AC,∠BAD=∠CAE,AD=AE,∴△ABD≌△ACE,∴∠B=∠C,又∵∠BOE=∠COD,BE=AB-AE=AC-AD=CD,∴△BOE≌△COD,∴OD=OE(2)∵△ABD≌

∵OE平分∠AOD∴∠AOE＝∠AOD/2∵OF平分∠BOC∴∠BOF＝∠BOC/2∵OA⊥OB∴∠AOB＝90∴∠EOF＝∠AOE+∠AOB+∠BOF＝∠AOD/2+∠BOC/2+90∵∠EOF＝1

OD⊥OE．∵OD平分∠AOC、OE平分∠BOC，∴∠DOC=12∠AOC，∠COE=12∠BOC，∴∠DOE=∠DOC+∠COE=12（∠AOC+∠BOC）=12×180°=90°，∴OD⊥OE．

∵OE平分∠AOD,OF平分∠BOD∴∠AOE=∠DOE,∠BOF=∠DOF∵∠EOF=∠DOE+∠DOF=25°∴∠AOD+∠BOD=2∠EOF=∠AOB=50°

证明：∵OE、OF分别平分∠AOC∠BOC∴∠EOC=1/2∠AOC；∠COF=1/2∠COB（角平分线的定义）又∵∠AOC+∠BOC=180°（补角的定义）∴∠EOF=∠EOC+∠COF=1/2∠A

∵OD平分∠BOC,∴∠COD=∠DOB,∵E平分∠AOC,∴∠COE=∠AOC,∴∠COD+∠EOC=∠AOE+∠DOB,∵∠AOB=180,∴∠EOD=90

∵AB与CD相交与O∴∠AOC+∠BOC=180°又∵∠BOC=∠AOC+30°∴∠AOC=75°,∠BOC=105°∵AB与CD相交与O∴∠BOD=∠AOC=75°∵OE平分∠BOD∴∠EOB=(1

设∠BOC=x°，则∠AOB=90°+x°，∵OD平分∠AOB，∴∠BOD=12（90-x）°，∵OE平分∠BOC，∴∠BOE=12x°，∴∠DOE=∠BOD-∠BOE=12（90-x）°-12x°=

在ΔOAD与ΔOCB中,OB=OD,OA=OC,∠AOD=∠BOC,∴ΔOAD≌ΔOCB(SAS),∴∠A=∠C,在ΔOAF与ΔODE中,OA=OC,∠A=∠C,∠AOF=∠COE,∴ΔAOF≌ΔCO

∵四边形ABCD中,BO=DOCO=AO∴▭ABCD∴AD∥BC,OA=OC,且∠AOF=∠ACB（或∠AFO=∠CEO）,又∵∠AOF=∠COE,∴△AOF≌△COE,∴OE=OF；是这

因为OE垂直于OF,所以角EOF=90度,即