Let's copy the diagram and highlight the segments we are asked to compare.
We can make some observations about the sides of the two triangles by using the fact that segments of equal length are congruent. Notice that two sides of △ TRQ are congruent to two sides of △ STR.
RQ≅ST
TR≅TR
However, the included angle in △ TRQ is larger than the included angle in △ STR. Therefore, by the Hinge Theorem, the third side of △ TRQ is longer than the third side of △ STR.
m∠ TRQ> m∠ STR
⇓
QT> RS
