From the given statements and reasons, we can deduce that ΔPMO ≅ ΔNMO because; it fulfils the ASA Congruence postulate.
We are given;
1) MO bisects ∠PMN
2) ∠PMO ≅ ∠NMO which means that ∠PMO is congruent to ∠NMO
3) MO ≅ MO
4) OM bisects ∠PON
5) ∠POM ≅ ∠NOM which means that ∠POM is congruent to ∠NOM
6) ΔPMO ≅ ΔNMO
Now, from all the statements given, we can see that two corresponding angles of both ΔPMO and ΔNMO are equal.
We also see that they share a common side which is MO.
Thus, we can say that both triangles have two corresponding sides that are equal and a corresponding included angle that is also equal.
In conclusion, ΔPMO ≅ ΔNMO because it fulfils the ASA Congruence postulate.
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