Question

Given the following congruent corresponding parts, choose all the congruent statements that apply.

MN ≅ QR, MP ≅ QS, PN ≅ SR
a. ∠PMN = ∠ASQR
b. ∠AMNP = ∠AQRS
c. ∠AMNP = ∠AQSR
d. ∠ANMP = ∠ARSQ

Answer 1

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.