The triangles would be congruent because of the two Triangle Congruence Theorms.
ASA: If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.
SAS: If any two angles and the included side are the same in both triangles, then the triangles are congruent.
Because your triangle has more than two angles that are congruent, and more than one side that are congruent, it more than fits the theorms.
Hope this helps.
