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Mathematical triangle ∠BAD=∠BCE BE=BD conjecture: △ the shape of △ACF
△ACF shape: isosceles triangle

Reason: AB=CB is obtained from AAS △ Abd △ CBE, while ∠BAC=∠BCA is obtained from "equilateral and isometric".

∠BAD=∠BCE ∠FAC=∠FCA ∠ FA=FC ∠ "Equiangular equilateral"

So △ACF is an isosceles triangle.