Question

What are the missing reasons in the two-column proof? Given: modifying above with right arrow upper M upper O bisects angle upper P upper M upper N and modifying above with right arrow upper O upper M bisects angle upper P upper O upper N Prove: triangle upper P upper M upper O congruent to triangle upper N upper M upper O

Answer 1

The missing reasons in the proof involve using the given bisections to apply the Angle-Side-Angle congruence criterion, demonstrating that triangles PMO and NMO are congruent.

Step-by-step explanation:

The question is regarding a geometric proof for the congruence of two triangles based on given bisecting lines.

To complete the two-column proof, you would use the given information that MO bisects ∠PMN and OM bisects ∠PON, which implies that ∠PMO = ∠NMO and ∠MOP = ∠MON.

By the Reflexive Property, we also know that segment OM is equal to itself. Hence, by the Angle-Side-Angle (ASA) congruence criterion, we can conclude that △PMO ≅ △NMO.