Congruency is a concept in geometry that refers to the similarity between two figures or objects. When two figures are congruent, it means that they have the same size and shape, and all their corresponding sides and angles are equal. In other words, they are identical in every way.

Congruency can be determined using different methods, such as comparing the lengths of sides and the measures of angles. The options provided in the question are different methods or criteria for determining congruency between two triangles.

- **ASS (Angle-Side-Side)**: This method states that if two angles and the side between them in one triangle are congruent to two angles and the side between them in another triangle, then the triangles are congruent. However, this method is not applicable in all cases and cannot guarantee congruency.

- **SSA (Side-Side-Angle)**: This method states that if two sides and the angle between them in one triangle are congruent to two sides and the angle between them in another triangle, then the triangles are congruent. However, this method is also not applicable in all cases and cannot guarantee congruency.

- **SAS (Side-Angle-Side)**: This method states that if two sides and the included angle in one triangle are congruent to two sides and the included angle in another triangle, then the triangles are congruent. This method is valid and guarantees congruency between the triangles.

Therefore, out of the given options, option C (SAS) is the correct answer as it is a valid criterion for proving congruency between triangles. The other options (ASS and SSA) may sometimes lead to false conclusions about congruency.

In summary:
- ASS (Angle-Side-Side) and SSA (Side-Side-Angle) are not always valid to prove congruency between triangles.
- SAS (Side-Angle-Side) is a valid method to determine congruency between triangles.