If △NMK ≅ △TRP, then △MNK ≅ △PTR by the corresponding parts of congruent triangles (CPCT) theorem.
If triangles △NMK and △TRP are congruent, it implies that their corresponding sides and angles are equal. The statement can be completed by considering the corresponding parts of these congruent triangles. According to the Corresponding Parts of Congruent Triangles (CPCT) theorem, corresponding angles and sides of congruent triangles are congruent.
Let's denote the vertices of the triangles: △NMK and △TRP. If △NMK ≅ △TRP, it means that ∠N ≅ ∠T, ∠M ≅ ∠R, and side NK ≅ side TP. Now, consider △MNK and △PTR. The corresponding parts of these triangles can be matched as follows:
1. Corresponding angles:
- ∠N (of △MNK) corresponds to ∠T (of △PTR) by CPCT.
- ∠M (of △MNK) corresponds to ∠R (of △PTR) by CPCT.
2. Corresponding side:
- NK (of △MNK) corresponds to TP (of △PTR) by CPCT.
Therefore, by CPCT, △MNK ≅ △PTR. The congruence statement is completed by identifying the corresponding angles and side between △NMK and △TRP, and then extending that congruence to △MNK and △PTR.