In triangles ABC and PQR, AB = QR, angle B = angle P, and BC = PR. Then:

Matching the vertices according to the given equal parts: $A$ corresponds to $Q$ (since $\angle B=\angle P$ means $B$ corresponds to $P$, and $AB=QR$ means $A$ corresponds to $Q$), $B$ corresponds to $P$, and $C$ corresponds to $R$. Thus, $\triangle ABC \cong \triangle QRP$.