Determine if the triangles in diagram 1 are congruent and if so, state the criterion.

Let's analyze the triangles in diagram 1.

We have two triangles, triangle ABC and triangle EDC. We are given that AC is congruent to EC, and BC is congruent to DC. Also, angle ACB is congruent to angle ECD because they are vertical angles.

Therefore, by the Side-Angle-Side (SAS) congruence criterion, triangle ABC is congruent to triangle EDC.

Answer: Yes, the triangles are congruent by the SAS criterion.