过点F作AC垂线FH交AC于点H
△BAD∽△BCA∽△GAF∽△ACD
CE是∠ACB的平分线,CE和高AD相交于点F
△CDF≌△CHF
得到:
AF:AG=AD:AB=AC:BC=CD:AC=CH:AC=FH:AE
即AG:AF=AE:FH
AE=AG*FH/AF
△CFH∽△CEA
FH:AE=CF:CE
AE=HF*CE/CF
即AG*FH/AF=HF*CE/CF
FG‖BC
BG:AG=DF:AF
BG=DF*GA/AF=AG*FH/AF=AE
过点F作AC垂线FH交AC于点H
△BAD∽△BCA∽△GAF∽△ACD
CE是∠ACB的平分线,CE和高AD相交于点F
△CDF≌△CHF
得到:
AF:AG=AD:AB=AC:BC=CD:AC=CH:AC=FH:AE
即AG:AF=AE:FH
AE=AG*FH/AF
△CFH∽△CEA
FH:AE=CF:CE
AE=HF*CE/CF
即AG*FH/AF=HF*CE/CF
FG‖BC
BG:AG=DF:AF
BG=DF*GA/AF=AG*FH/AF=AE