Identify side lengths of Triangle ABC

List the side lengths of triangle ABC in increasing order: $AB = 5$, $BC = 12$, $AC = 13$.

$\text{Sides of } \Delta ABC: 5, 12, 13$

Identify side lengths of Triangle PQR

List the side lengths of triangle PQR: $QR = 5$, $PQ = 12$, $PR = 13$.

$\text{Sides of } \Delta PQR: 5, 12, 13$

Map corresponding vertices

Match the vertices based on side equality: The side of length 5 is $AB$ in $\Delta ABC$ and $QR$ in $\Delta PQR$. The side of length 12 is $BC$ in $\Delta ABC$ and $PQ$ in $\Delta PQR$. This implies the correspondence $A \leftrightarrow Q$, $B \leftrightarrow R$, and $C \leftrightarrow P$.

$\Delta ABC \cong \Delta QRP$

Verify against options

The order of vertices that maintains the correspondence is $A \to Q$, $B \to R$, $C \to P$. Thus, $\Delta ABC \cong \Delta QRP$.

$\Delta ABC \cong \Delta QRP$