It is known that, as shown in the figure, the vertices of the equilateral triangle def are on the edges of the equilateral triangle ABC. Proof: ad = be = CF

Let D, e, f be on the sides AB, BC, AC respectively. ∵ △ ABC, △ def be regular triangle, ∵ a = ∵ B = ∵ C = 60 ∵ EDF = ∵ fed = ∵ EFD = 60 ∵ de = DF = EF ? BDE + ? ADF = 180-60 = 120 ? ADF + M AFD = 180-60 = 120 ? AFD = ≌ BDE ≌ ADF ≌ be = CF

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