Question

梯形ABCD,AD//BC、AB=CD,对角线AC、BD交于O

Answer 1

∵△ABC∽△CFP

∴EP:AB=CP:BC

∵△BDC∽△BPE

∴PE:DC=BP:BC

∵AB=CD

∴（EP:AB）+（PE:DC）=（EP:AB)+(PE:AB)=（CP:BC）+（BP:BC）=1

∴（EP:AB)+(PE:AB)=1

等式两边同乘以AB可得到：PE+PF=AB