There are four ways to dissect a triangle into three triangles, and in all cases (at least) two of them share a common side. By chasing angles, I cannot see other cases for the three partition triangles being equal but for the original triangle being equilateral, or right-angled, with the other two angles being $ 30$ and $ 60$ degrees!

does equal triangles mean congruent triangles or triangles with equal area?