If the altitudes $\text{AD},\text{ BE}$  and $\text{CF}$ of a triangle $\text{ABC}$ are equal, then the triangle $\text{ABC}$ is

By RHS congruency,

$\Delta FCB\cong \Delta EBC$

By CPCT, $\angle FBC=\angle ECB$

$\angle ABC=\angle ACB$ ($\because$ by angle property)

$AC=AB$

Similarly $AB=BC$

Then $AB=BC=CA$

$\therefore$  $\Delta ABC$  is equilateral.