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.A two column proof is shown. In the statements column there are 6 statements. 1 says modifying above with right arrow upper M upper O bisects angle upper P upper M upper N. 2 says angle upper P upper M upper O congruent to angle upper N upper M upper O. 3 says modifying above with bar upper M upper O congruent to modifying above with bar upper M upper O. 4 says modifying above with right arrow upper O upper M bisects angle upper P upper O upper N. 5 says angle upper P upper O upper M congruent to angle upper N upper O upper M. 6 says triangle upper P upper M upper O congruent to triangle upper N upper M upper O. In the reasons columns there are the numbers 1 through 6 but each reason is blank with a question mark. The diagram is also shown. Line upper M upper O is horizontal across the middle of the diagram. Point upper N is at the top of the diagram and two lines extend from it down to line upper M upper O forming a triangle. Another point upper P is at the bottom of the diagram and two lines extend from it up to line upper M upper O forming another triangle. The two triangles appear congruent and share two vertices on line upper M upper O.
(6 points)
The missing reasons in the two-column proof are:
1. Definition of angle bisector
2. Corresponding angles of congruent triangles are congruent (CPCTC)
3. Reflexive property of congruence
4. Definition of angle bisector
5. Corresponding angles of congruent triangles are congruent (CPCTC)