In order to prove that two triangles are congruent - so that the triangles can fit over each other, possible after a rotation or reflection or both - we need the triangles to have three features that are the same, with at least one of them being a length. These could be

1. Three sides

2. Two sides and an angle, with these features on each triangle arranged the same relative to one another

2. One side and two angles, with these features on each triangle arranged the same relative to one another

If triangles have corresponding identical angles, they may or may not be congruent. A triangle may be larger than another triangle having identical corresponding angles. Obviously these triangles are not congruent. They are similar.