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 Triangles

The triangles are congruent by the Angle - Side - Angle (ASA) congruence criterion.

Step2: List Congruent Parts

• $\angle M\cong\angle C$ (Given)
• $MN = CA$ (Given)
• $\angle N\cong\angle A$ (Given)

Step3: Apply ASA Criterion

Since two angles and the included side of $\triangle MNO$ are congruent to two angles and the included side of $\triangle CBA$, by ASA, $\triangle MNO\cong\triangle CBA$.

Answer:

The triangles are necessarily congruent. The first three boxes should be filled with:

• $\angle M\cong\angle C$ (Type of Statement: Angle Congruence)
• $MN = CA$ (Type of Statement: Side Congruence)
• $\angle N\cong\angle A$ (Type of Statement: Angle Congruence)

The reason for $\triangle MNO\cong\triangle CBA$ is ASA (Angle - Side - Angle).