As shown in the figure, △ ACD, △ Abe, △ BCF are equilateral triangles on the same side of the straight line BC. (1) when ab ≠ AC, it is proved that the quadrilateral ADFE is a parallelogram; (2) when AB = AC, what kinds of graphs are formed by successively connecting four points a, D, F and E? Write directly the types and corresponding conditions of the figures

(1) It is proved that: ∵ Abe, △ BCF are equilateral triangles, ∵ AB = be = AE, BC = CF = FB, ∵ Abe = ∠ CBF = 60 °. ∵ CBA = ∠ FBE. ≌ ABC ≌ EBF. ≌ EF = AC. ADCs are equilateral triangles,

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