Given the figure on the problem, let's try to analyze the corresponding reason for each statements to be true.
The first statement says that MO bisects ∠PMN. This is given in the problem, hence, for the first statement the reason is given.
The second statement says that ∠PMO≅∠NMO. The two angles become congruent due to the bisector line MO, hence, the reason behind this statement is definition of angle bisector.
The third statement says that MO ≅ MO. This is due to reflexive property.
The fourth statement states that OM bisects ∠PON. This is given in the problem.
The fifth statement states that ∠POM≅∠NOM. This is the same as statement two, which is due to definition of angle bisector.
The last statement states that ΔPMO ≅ ΔNMO. Due to the congruence stated from second and fifth statement, this statement can be reasonable due to SAS postulate.
Hence, the completed two-column proof is
