Question

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. diagram - related dropdowns and statements about congruence with reasons given and a final statement △lmn≅△baz with a reason - select dropdown

Explanation:

Step1: Identify congruent parts

From the diagram, we can see that $\angle A\cong\angle M$ (marked with one - arc), $\angle Z\cong\angle N$ (marked with two - arcs), and $AZ\cong MN$ (marked with one segment).

Step2: Determine congruence criterion

The Angle - Angle - Side (AAS) congruence criterion states that if two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, then the two triangles are congruent. Here we have two pairs of congruent angles and a pair of congruent non - included sides.

Answer:

The first box: $\angle A\cong\angle M$, Reason: GIVEN
The second box: $\angle Z\cong\angle N$, Reason: GIVEN
The third box: $AZ\cong MN$, Reason: GIVEN
For $\triangle LMN\cong\triangle BAZ$, Reason: AAS