Question

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.
the triangles are necessarily congruent.
δklm ≅ δazy

Explanation:

Step1: Identify corresponding parts

In \(\triangle KLM\) and \(\triangle AZY\), from the diagram, we can see that \(KL = AZ\) (marked with one tick), \(LM=ZY\) (marked with two ticks), and \(\angle M=\angle Y\) (marked with an arc).

Step2: Apply congruence criterion

By the Side - Angle - Side (SAS) congruence criterion. If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent. Here, in \(\triangle KLM\) and \(\triangle AZY\), \(KL = AZ\), \(LM = ZY\), and \(\angle M=\angle Y\) (the included angle between \(LM\) and \(KM\) in \(\triangle KLM\) and between \(ZY\) and \(AY\) in \(\triangle AZY\)).

Answer:

The reason for \(\triangle KLM\cong\triangle AZY\) is the Side - Angle - Side (SAS) congruence criterion.