Final answer:
Analyzing congruent segments MN ≡ QR, MP ≡ QS, and PN ≡ SR, only statement a. ∠PMN = ∠ASQR is correct because the triangles MPN and QSR are congruent by the SSS criterion, making their corresponding angles congruent.
Step-by-step explanation:
The question is asking to determine which congruent statements are correct based on the given congruent corresponding parts MN ≡ QR, MP ≡ QS, and PN ≡ SR. Analyzing the given information, we can say:
- Option a. ∠PMN and ∠ASQR are congruent because MP ≡ QS and PN ≡ SR, making triangles MPN and QSR congruent by SSS (side-side-side) criterion. Therefore, the corresponding angles ∠PMN and ∠ASQR are congruent.
- Options b. and c. contain an error because there is no vertex 'A' in the given sides, thus the angle names starting with 'A' are not applicable.
- Option d. ∠ANMP and ∠ARSQ are not congruent either, as 'A' is not part of the given congruent sides.
Only congruent statement from the provided options that can apply is a. ∠PMN = ∠ASQR based on the given congruent side lengths making the triangles congruent.