I can only say that the conclusion given on the Internet (2) may be wrong. I can only say that EB=EF I proved it, but ed and EF really didn't find any relationship! Furthermore, when the general questioner makes a question, (2) and (3) should correspond, so I think this conclusion is different from the original volume.

I can say EB=EF (take a little g on AB to make AE=AG and connect GE.

△BGE and△△ EDF, BG = ED, ∠ GBE+∠ AEB = 2A, ∠ AEB+∠ DEF = 2A, so ∠GBE=∠DEF.

∠ EDF = 180-A, Ag = AE, ∠ Age = ∠ AEG, ∠AGE=a, ∠ BGE = 180-A, so ∠EDF =∞.

So △BGE and △EDF are congruent, and EB=EF.

(3)BE/EF=n-m+ 1

Extend AB to h, make AH=AE, connect EH,

AB=mDE and AH = AE, AH = AB+BH = AE = MDE+BH, AE = AD+DE and AD=nDE, so BH=(n+ 1-m)DE.

In △EBH and FED, ∠ A = 180-2A, AE=AH, ∠H=∠AEH, so ∠H=a, and ∠EDF=∠C=a, then:.

Because AD//BC, ∠EBC=∠DEB, ∠ BEF = 180-2A, ∠ HBC = 180-2A, ∠HBE=∠DEF.

So △EBH is similar to the Federal Reserve, so BE/EF=AH/DE=n-m+ 1.