To prove triangles congruent using the Side-Side-Side (SSS) congruence criterion, you need to know that all three corresponding sides of the triangles are equal in length.
Given the choices:
- PR = DF (this states one pair of corresponding sides is equal)
- ∠P = ∠D (this states one pair of angles is equal, which is not useful for SSS)
- ∠Q = ∠E (this states another pair of angles is equal, which is also not useful for SSS)
- QR = EF (this states another pair of corresponding sides is equal)
To apply SSS, you need the lengths of all three corresponding sides. According to the information you provided, you need to confirm that QR = EF as well as another side pair.
Thus, you should ensure that PR = DF, QR = EF, and you also need the length of the last corresponding side PQ = DE.
If that length is known or can be established, then you would have all the information you need for SSS congruence.