Final answer:
Without details on the sides and angles of triangles PQR and RQS, we cannot determine the correct postulate or theorem (AAS, SSS, SAS, ASA) to prove congruency.
Step-by-step explanation:
To determine which postulate or theorem can prove that triangles PQR and RQS are congruent, we need to compare the given sides and angles of the triangles. The options presented to us are Angle-Angle-Side (AAS), Side-Side-Side (SSS), Side-Angle-Side (SAS), and Angle-Side-Angle (ASA). Unfortunately, the original question does not provide specific details about the sides and angles of triangles PQR and RQS. Therefore, without additional information on the triangles themselves, we cannot confidently select the correct postulate or theorem to prove the congruency.
It is essential in geometry to closely assess the given information to apply the correct postulates. These foundational rules ensure that our geometric reasoning is precise and leads us to correct conclusions, just as in physics, where postulates must accurately describe nature.