Final answer:
Without the specific measurements or properties of triangles △PNQ and △QRP, we cannot determine whether the ASA Postulate, SSS Postulate, SAS Postulate, or AAS Theorem proves the congruence of the triangles.
Step-by-step explanation:
The student has asked which postulate or theorem proves that triangles △PNQ and △QRP are congruent. To determine which one applies, we need to consider the information given about the triangles. If we have information on two angles and a side (ASA or AAS) or three sides (SSS) or two sides and an angle between them (SAS) for both triangles, then we can identify the specific postulate or theorem.
ASA Postulate asserts that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. SAS Postulate 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, then the two triangles are congruent. SSS Postulate requires three pairs of congruent sides to prove triangle congruence. Lastly, the AAS Theorem states that if two angles and a non-included side of one triangle are congruent to two angles and a corresponding non-included side of another triangle, then the triangles are congruent.
Without specific information on the sides and angles of triangles △PNQ and △QRP, we would not be able to choose from these options. However, as per the provided details in the question, it seems this information is missing or not provided. Therefore, to choose the correct postulate or theorem, we need the measurements or properties of the corresponding parts of △PNQ and △QRP.
In conclusion, based on the given information in the question, we cannot determine which postulate or theorem proves that △PNQ and △QRP are congruent as the necessary information on sides and angles is absent. If the necessary details are available, one can revisit the options A through D to establish the correct congruence criterion.