Question

which shows two triangles that are congruent by the sss congruence theorem?

Explanation:

Step1: Recall SSS congruence theorem

The SSS (Side - Side - Side) congruence theorem states that if the three sides of one triangle are equal in length to the three corresponding sides of another triangle, then the two triangles are congruent. We need to look for the option where the three pairs of sides of the two triangles are marked as equal.

Step2: Analyze each option

In the first option, there are right - angle markings and single - line markings, but not three pairs of side - length equalities for SSS. In the third option, there are angle markings and single - line markings, not sufficient for SSS. In the second option, we can see that \(AB = DE\), \(BC=DC\), and \(AC = EC\) as indicated by the side - length markings. This satisfies the SSS congruence theorem.

Answer:

The second option shows two triangles that are congruent by the SSS congruence theorem.