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 given information

We are given that \( \angle Z=\angle L\) (from the angle markings), \( ZA = KL\) (from the side - length markings), and \( \angle A=\angle K\) (from the angle markings).

Step2: Apply ASA (Angle - Side - Angle) congruence criterion

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

• \( \angle Z=\angle L\) (given)
• \( ZA = KL\) (given)
• \( \angle A=\angle K\) (given)

Since \(ZA\) is the included side between \(\angle Z\) and \(\angle A\) in \(\triangle ZAY\), and \(KL\) is the included side between \(\angle L\) and \(\angle K\) in \(\triangle KLM\), by the ASA congruence criterion, \(\triangle ZAY\cong\triangle KLM\)

Answer:

The two triangles are necessarily congruent. The flowchart proof (using ASA) would have the following statements (in order): \(\angle Z\cong\angle L\) (Reason: GIVEN), \(ZA\cong KL\) (Reason: GIVEN), \(\angle A\cong\angle K\) (Reason: GIVEN), and then \(\triangle ZAY\cong\triangle KLM\) (Reason: ASA (Angle - Side - Angle) Congruence Theorem)