In triangles DEF and PQR, if DE = PQ, EF = QR, and FD = RP , which congruence criterion shows that triangle DEF is congruent to triangle PQR?

Correct Option: SSS

Step-by-step Explanation:

To determine which congruence criterion shows that triangle DEF is congruent to triangle PQR, let us analyze the given information about their corresponding side lengths:

1. DE = PQ (The first side of triangle DEF is equal in length to the corresponding side of triangle PQR)

2. EF = QR (The second side of triangle DEF is equal in length to the corresponding side of triangle PQR)

3. FD = RP (The third side of triangle DEF is equal in length to the corresponding side of triangle PQR)

The Side-Side-Side (SSS) congruence criterion states that if three sides of one triangle are equal to the three corresponding sides of another triangle, then the two triangles are congruent.

Since all three corresponding sides of triangle DEF and triangle PQR are equal, triangle DEF is congruent to triangle PQR by the SSS congruence criterion.