What does it mean for triangles to be "congruent"?

For triangles to be considered congruent, they must be identical in both size and shape. This means that all corresponding sides are equal in length, and all corresponding angles are equal in measure. The congruence of triangles indicates that if you were to superimpose one triangle over the other, they would perfectly overlap without any discrepancies.

This definition addresses the fundamental characteristics needed for triangles to be congruent, which includes having corresponding angles of equal measurements and sides of equal lengths. Understanding this concept is crucial in geometry, as it forms the basis for various theorems and properties related to triangles and their relationships.

In contrast, if triangles had different sizes, the idea of congruency would not apply. Additionally, having the same dimensions alone does not account for the arrangement or angles of the triangles, which is essential in determining congruence. Lastly, merely sharing one angle does not establish congruence since two triangles can share an angle yet differ in size and shape. Therefore, congruency encompasses a complete match of all corresponding parts, affirming that the answer highlighting equal angles and sides is indeed correct.