1. **Stating the problem:** We are given two triangles ONM and UVS with corresponding parts congruent: ON \cong UV, NM \cong TU, MP \cong VS, and \angle P \cong \angle V. We want to analyze the congruence and relationships between these triangles. 2. **Understanding congruence:** When two triangles are congruent, all corresponding sides and angles are equal. Here, the given congruences suggest that triangles ONM and UVS are congruent by the Side-Angle-Side (SAS) or Side-Side-Side (SSS) criteria. 3. **Given side lengths:** - Triangle ONM: ON = 15 in, NM = 8 in, OP = 26 in (assuming OP corresponds to side OM) - Triangle UVS: UV = 8 in, TU = 15 in, VS = 26 in 4. **Matching sides:** Since ON \cong UV and NM \cong TU, and MP \cong VS, the sides correspond as ON = UV = 15, NM = TU = 8, and MP = VS = 26. 5. **Conclusion:** The triangles ONM and UVS are congruent by SSS congruence criterion because all three pairs of corresponding sides are equal. **Final answer:** Triangles ONM and UVS are congruent by SSS congruence.