Question

In triangles DEF and OPQ, ∠D ≅ ∠O, ∠F ≅ ∠Q, and segment DF ≅ segment OQ. Is this information sufficient to prove triangles DEF and OPQ congruent through SAS? Explain your answer.

Option 1: Yes, the information is sufficient.
Option 2: No, more information is needed.

Answer 1

No, the information is not sufficient to prove congruence through SAS.

Step-by-step explanation:

No, the information is not sufficient to prove triangles DEF and OPQ congruent through SAS. SAS (Side-Angle-Side) congruence requires that two triangles have two pairs of corresponding sides that are congruent and the included angles between those sides are congruent. While we know that segment DF is congruent to segment OQ and that ∠D is congruent to ∠O, we do not have enough information about the remaining sides and angles to prove congruence.