III. Direction: Determine the congruent parts of \( \triangle \mathrm{PQR} \cong \) \( \triangle \mathrm{XYZ} \).

In congruent triangles, corresponding parts are equal. For \( \triangle PQR \cong \triangle XYZ \), it means that the angles and sides of both triangles match up perfectly. This implies that \( \angle P \) is congruent to \( \angle X \), \( \angle Q \) to \( \angle Y \), and \( \angle R \) to \( \angle Z \). Additionally, the side lengths must also correspond: \( PQ \cong XY \), \( QR \cong YZ \), and \( RP \cong ZX \). This concept is super useful in real-world applications such as architecture and engineering, where the stability and symmetry of structures are designed by ensuring that parts are congruent. For instance, in designing a bridge, engineers often need to calculate angles and dimensions that ensure each side is equal and contributes to the overall stability of the structure.