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 all three pairs of corresponding sides are marked as equal.

Step2: Analyze each option

In the first option, we have right - angle markings and some side - length markings but not all three sides of the two triangles are clearly marked as equal. In the third option, we have angle markings and side - length markings but not all three sides of the two triangles are marked as equal. In the fourth option, we only have one pair of sides marked as equal. In the second option, we can see that \(AB = DE\), \(AC=CE\) and \(BC = CD\) (the markings on the sides indicate equality), which satisfies the SSS congruence theorem.

Answer:

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