Final answer:
Two congruent interior angles do not suffice to confirm similarity of triangles unless they fulfill the Angle-Angle (AA) postulate, confirming that all corresponding angles are equal and sides are proportional.
Step-by-step explanation:
If two corresponding interior angles of two triangles are congruent, this alone does not guarantee that the triangles are similar. However, if you can determine that the triangles also have their sides in proportion, or if the two congruent angles are part of a series of corresponding angles that are all congruent between the two triangles, then according to the Angle-Angle (AA) similarity postulate, the triangles are similar.
This means that all their corresponding angles are equal and the lengths of their corresponding sides are proportional.
The concept of triangles being similar is a foundational idea in geometry and is based on specific criteria such as the Angle-Angle postulate.