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 sides and angles

From the diagram, we can see that \(ZA\cong KL\) (given as the sides with double - hash marks), \(ZY\cong ML\) (given as the sides with single - hash marks), and \(\angle Z\cong\angle L\) (given as the angles with the same marking).

Step2: Apply the SAS (Side - Angle - Side) congruence criterion

The SAS congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
In \(\triangle ZAY\) and \(\triangle KLM\), we have:

• \(ZA = KL\) (side)
• \(\angle Z=\angle L\) (included angle)
• \(ZY = ML\) (side)

Answer:

The two triangles \(\triangle ZAY\) and \(\triangle KLM\) are congruent by the SAS (Side - Angle - Side) congruence criterion.