设AD // BE // CF,其中A,B,C共线,D,E,F共线.
AB:BC = S△DAB:S△DBC (同高三角形面积比等于底之比).
∵AD // BE,∴S△DAB = S△DAE (二者同底等高).
同理∵AD // CF,∴S△DAC = S△DAF.
∴S△DBC = S△DAC-S△DAB = S△DAF-S△DAE = S△AEF.
又∵S△DAE:S△AEF = DE:EF (同高三角形面积比等于底之比),
∴AB:BC = DE:EF.