Given QT = SR, QV = SU, and the diagram below, prove that triangles QUT and SVR are congruent. Write a paragraph proof.

To prove that triangles QUT and SVR are congruent, we can use the Side-Side-Side (SSS) Congruence Criterion. We know from the given information that QT = SR and QV = SU, which provides us with two pairs of equal sides. To complete the SSS criteria, we need to prove that side QU is equal to side SV. Since point U lies on line QT and point V lies on line SR, by the given equality of segments, and assuming that point U corresponds to point S and point V corresponds to point R in their respective triangles, the segment QU must equal segment SV. Thus, we have established that QT = SR, QV = SU, and QU = SV. Consequently, all three sides of triangle QUT are congruent to the three sides of triangle SVR. Therefore, by the SSS Criterion, triangles QUT and SVR are congruent.