The SSS (Side-Side-Side) congruence theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.
From the options provided, the correct choice that shows two triangles congruent by the SSS theorem is:
Triangles A B C and D E C are connected at point C. The lengths of sides A B and D E are congruent. The lengths of sides B C and C D are congruent.
This option specifies that two sides are congruent with respect to the two triangles, and since they share the common side C (which we assume also has a length), all three corresponding sides are congruent, thereby confirming that the triangles are congruent by the SSS theorem.