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.
$\angle a \cong \angle o$
reason: given
$\angle c \cong \angle m$
reason: given
$\overline{ca} \cong \overline{mo}$
reason: given

Explanation:

Step1: Identify given congruences

Given: $\angle A \cong \angle O$, $\angle C \cong \angle M$, $\overline{CA} \cong \overline{MO}$

Step2: Match to congruence rule

The ASA (Angle-Side-Angle) congruence rule states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent. Here, $\angle A$ and $\angle C$ are the two angles of $\triangle ABC$, with included side $\overline{CA}$; these correspond to $\angle O$, $\angle M$, and included side $\overline{MO}$ of $\triangle ONM$.

Step3: Conclude triangle congruence

By ASA congruence, $\triangle ABC \cong \triangle ONM$.

Answer:

The triangles are necessarily congruent.
$\triangle ABC \cong \triangle ONM$ by the ASA Triangle Congruence Postulate.