jimthompson5910

The two column proof is shown below in the attached image.

We start listing the given statements exactly as they are presented. It may seem silly to restate what is already told, but think of the two column proof as something you can pull away from the instructions and have it be fully independent on its own (though you'll often bring along the diagram).

After we list all the given info, we then would use the AAS (angle angle side) triangle congruence theorem. This is different from ASA because the side (S) is not between the two angles (A). For triangle MNO, the side with the tickmark is not between the two angles marked for this triangle. A similar story happens with triangle PQR as well.

Lastly, we then use CPCTC (corresponding parts of congruent triangles are congruent) to conclude that angle O and angle R are congruent to one another.

The last line of any two column proof is always the statement we want to prove.