Question

determine if the two triangles are necessarily congruent. if so, fill in a flowchart proof to prove that they are. the triangles are necessarily congruent. for each of the first three boxes, choose a statement format from the dropdown menu. you will then be able to change the letters to match the diagram for this problem.

Explanation:

Step1: Identify congruent parts

We see that $\angle A=\angle O$, $\angle C=\angle M$, and $AC = OM$ (marked in the diagram).

Step2: Apply congruence criterion

By the Angle - Angle - Side (AAS) congruence criterion, if two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, the triangles are congruent. Here, in $\triangle CBA$ and $\triangle MNO$, we have two pairs of congruent angles and a pair of congruent non - included sides.

Answer:

The triangles are necessarily congruent.
First box: $\angle A=\angle O$ (Given)
Second box: $\angle C=\angle M$ (Given)
Third box: $AC = OM$ (Given)
Bottom box: Reason: AAS (Angle - Angle - Side) congruence criterion.