I have a negative answer. The angles $ \alpha =\alpha'$,$ \beta =\beta'$, $ \gamma =\gamma'$ are equal if and only if the corresponding least angles ($ <90^o$) between the medians and the respective side are equals. But the last condition its true for the following triangles. Take any triangle $ ABC$, and the triangle $ A'B'C'$ such that its sides are the medians of $ ABC$ (we can construct it by an easy way), it is not hard to prove that for this two triangles the conditions of the problem holds, but they doesn't have to be similar.