Suppose there is such a triangle that satisfies the known conditions, but △ABC is not equilateral △

Let ∠A be the largest among ∠A, ∠B and ∠C, then BC is larger than the other two sides, namely, BE & gtCF and BE> in the year 200.

So ∠BDE is the largest of the three corresponding angles, that is ∠ BDE >; ∠CEF and ∠ BDE > ∠AFD .

And ∠ bde+∠ ADF =120 = ∠ cef+∠ bed = ∠ AFD+∠ cfe,

So ∠ADF is the smallest of the three corresponding angles, so ∠ ADF < ∠DEB.

According to sine theorem:

sin∠A:sin∠ADF = DF:AF = DE:BD = sin∠B:sin∠DEB

And < ∠A>；; ∠B，∠ADF & lt； Debt

So sin ∠ a: sin ∠ ADF >: sin∠B:sin∠DEB.

This contradicts the previous equation, so there is no non-regular triangle that meets the conditions.

So △ABC is a regular triangle.