ABCD is rectangular, so AP‖BE.

∠APF=∠EBF

F is the midpoint of AE, and AF=EF.

Afp =∠EFB

So △ AFP △ EFB

So AP=BE, PF=BF.

PD=AP+AD，CE=BC+BE

So PD=CE

Because ABCD is rectangular, CA=BD=CE.

So PD=BD, and the triangle PBD is an isosceles triangle.

DF is the center line of the bottom BP, so it is also the height on the BP.

So BF⊥DF