In the trapezoid ABCD, ad ∥ BC, BF = FG = GC, it is proved that AP: FP = AF: ef (P is a point under the bottom edge of the trapezoid, AP intersects at point F through BC, DP intersects at point G through BC, and the intersection of BD and AP is e) BC is a trapezoid. The bottom (long) edge of ABCD is below the trapezoid, that is, BC

⊿ADP∽⊿FGP,
AP∶FP＝AD∶FG＝AD∶BF.
⊿EAD∽⊿ EFB.AD ∶BF＝AE∶EF.
The results showed that AP ∶ FP = AE ∶ EF
(if the result is correct, AP: FP = AF: EF. Then AE = AF. No. It's estimated that the swallow loves apples, and the wrong number makes AE AF.)

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