To determine the condition for the congruence of triangles \( \Delta PQR \) and \( \Delta ABC \), we need to analyze the given information:

• \(\angle A = \angle P\)
• \(AC = PR\)

We are required to find which additional condition is needed for congruence.

The congruence criteria involved are:

• SAS (Side-Angle-Side): Two sides and the included angle are equal.
• ASS/SSA: Generally not valid for proving congruence except in the specific case of right triangles (HL).

Given that \(\angle A = \angle P\) and \(AC = PR\), if we have \(AB = PQ\), then we can use the SAS congruence criterion since we have two sides and the included angle equal.

Hence, the condition AB = PQ by SAS criteria must be satisfied for \(\Delta PQR\) and \(\Delta ABC\) to be congruent.

Let's analyze why other options don't work:

• BC = QR by ASS criteria: ASS is not a valid criterion for congruence.
• BC = QR by SSA criteria: Same as above; SSA does not prove congruence.
• AB = PQ by SSA criteria: Again, SSA is not a valid rule for congruence.

Thus, the correct answer is: AB = PQ by SAS criteria.