Question

Which of the following congruence statements is accurate regarding triangles ∆PMQ and ∆RMS?

a. ∆PMQ ≅ ∆RMS by SAS congruence because QM = SM, PM = RM, and ∠PMQ = ∠QMR
b. QM = SM, PM = RM, and ∠PMQ = ∠RMS
c. QM = SM, SR = QR, and ∠PMQ = ∠QMR
d. None of these

Answer 1

The correct congruence statement regarding triangles ∆PMQ and ∆RMS is that ∆PMQ ≅ ∆RMS by SAS congruence.

Step-by-step explanation:

The correct congruence statement regarding triangles ∆PMQ and ∆RMS is option a. ∆PMQ ≅ ∆RMS by SAS congruence because QM = SM, PM = RM, and ∠PMQ = ∠QMR.

We can use the SAS (Side-Angle-Side) congruence criteria to prove that the two triangles are congruent. In this case, we have the following:

1. Side QM = Side SM
2. Side PM = Side RM
3. Angle ∠PMQ = Angle ∠QMR

Since all three conditions are satisfied, we can conclude that the two triangles ∆PMQ and ∆RMS are congruent by SAS congruence.