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 the congruent sides and angles

From the diagram, we can see that \(OM = CB\) (given), \(MN=CA\) (given), \(\angle OMN=\angle BCA\) (given).

Step2: Apply the congruence criterion

Since we have two sides and the included angle of one triangle equal to two sides and the included angle of another triangle, we use the Side - Angle - Side (SAS) congruence criterion.

Answer:

The first three boxes should be filled with:

• \(OM = CB\) (Reason: GIVEN)
• \(\angle OMN=\angle BCA\) (Reason: GIVEN)
• \(MN = CA\) (Reason: GIVEN)

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