I think you missed the point of the question. It does not ask that the solver prove either of the two statements, or their converses, merely to state which part is proven. (The first statement, and it's converse are, in any case, not amenable to mathematical proof, though they can still be analysed for their logical content, which is the point of the question.)

The second statement can be restated as

Code:

IF a triangle is equilateral THEN it is equiangular.

The 'given' part is that the triangle is equilateral. The 'proven' part is that it is equi-angular.

The converse is the same statement written with 'given' and 'proven' parts reversed:

Code:

IF a triangle is equiangular THEN it is equilateral.

.

or, using the form of the original statement:

Code:

Every equiangular triangle is equilateral.

The solver is asked to determine whether this is true of false. He is not asked to prove it, so I think a bare assertion is sufficient: It's true.