Answer
According to the Hinge Theorem, if two consecutive sides in a triangle are congruent to two consecutive sides in another triangle, but their included angles are not congruent, then the side that is opposite to the larger included angle is longer than the side that is opposite the smaller included angle.
$\overline{PQ}$ in $\triangle QPT$ is congruent to $\overline{TR}$ in $\triangle QRT$, and $\overline{QT}$ in $\triangle QPT$ is congruent to $\overline{QT}$ in $\triangle QRT$ ($\overline{QT}$ is common to both triangles).
The included angle of $\triangle QPT$, $\angle PQT$, is $90^{\circ}$ (because it is a right angle) whereas the included angle of $\triangle QRT$, $\angle RTQ$, is $92^{\circ}$; therefore, $\angle RTQ$ is the bigger angle, and the side opposite to it ($\overline{QR}$) will be the longer side.
$\overline{PT}$ < $\overline{QR}$
Work Step by Step
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