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
A two column proof and a diagram are shown.
Unfortunately, you did not provide the two-column proof or the diagram. Without that information, it is not possible to determine the missing reasons in the proof. Please provide the two-column proof and the diagram for further assistance.
I'm sorry, but without the actual two-column proof and the accompanying diagram, I can't provide you with the missing reasons. Can you please provide the two-column proof and the diagram, or give more specific information about the missing reasons?
To determine the missing reasons in the two-column proof, we first need to understand the statements and the given information. The given information states that segment MO bisects angle PMN, and segment OM bisects angle PON. We are then asked to prove that triangle PMO is congruent to triangle NMO.
To complete a two-column proof, we need to provide a reason for each statement made. The reasons should be logical and based on previously proven theorems, definitions, or properties of geometric figures. Without the specific statements from the proof and the diagram, it is not possible to determine the missing reasons accurately.
However, here are some possible reasons that could be used to prove the congruence of the two triangles, based on the given information:
1. Definition of angle bisector: Segment MO bisects angle PMN.
2. Definition of angle bisector: Segment OM bisects angle PON.
3. Common side: Segment OM is common to both triangles PMO and NMO.
4. Angle-side-angle (ASA) Congruence Criteria: With angle PMN congruent to angle MNO (as a result of angle bisectors), segment OM congruent to itself, and angle POM congruent to angle NOM (vertical angles), triangle PMO is congruent to triangle NMO.
It is important to note that the specific reasons and steps of the proof may vary depending on the given statements and diagram.