what are missing reasons in the two collumnproof given: MO bisects <PMN and OM bisects <PON Prove: PMO = NMO
In order to prove that PMO = NMO given MO bisects <PMN and OM bisects <PON, we need to include the following missing reasons in the proof:
1. Given: MO bisects <PMN
2. Given: OM bisects <PON
3. MO bisects <PMN implies that angles PMO and NMO are congruent (definition of angle bisector).
4. OM bisects <PON implies that angles POM and NOM are congruent (definition of angle bisector).
5. Angles PMO and POM are vertical angles (definition of vertical angles).
6. Angles NMO and NOM are vertical angles (definition of vertical angles).
7. Vertical angles are congruent.
8. Therefore, PMO = NMO (transitive property of equality).