Question

平行线分线段成比例!

Answer 1

AB:EF=DB:DF

(AB-EF):EF=(DB-DF):DF

(AB-EF):EF=BF:DF

EF:(AB-EF)=DF:BF

(EF+AB-EF):(AB-EF)=(DF+BF):BF

AB:(AB-EF)=BD:BF=CD:EF

AB:(AB-EF)=CD:EF

a:(a-c)=b:c

ac=ab-bc

ab=bc+ac,

两边同除以ab:

1=c/a+c/b,

两边同除以c:

1/c=1/a+1/