Question

What are the missing reasons in the two-column proof?

Answer 1

Reasons:

1. Because, MO cuts Angle PMN in two equal parts.

2.As ∠PMN is cut in to equal parts thus:

∠PMN = ∠NMO + ∠PMO, where these two parts (∠NMO, ∠PMO) are equal.

3. Both are the same, common you can say..

4. Because, MO cuts Angle PON in two equal parts.

5. As ∠PON is cut in to equal parts thus:

∠PON = ∠NOM + ∠POM, where these two parts (∠NOM , ∠POM) are equal.

6. From the above statements, we have:

= ∠NMO + ∠PMO (Proved)

= ∠NOM + ∠POM (Proved)

= MO = MO (Proved)

Thus, ∆PMO ≅ ∆NMO, by AAS rule

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As simpoool as that!