determine if the two triangles are necessarily congruent. if so, fill in a flowchart proof to prove that…

Explanation:

Step1: Analyze triangle markings

In $\triangle ABZ$ and $\triangle NLM$:

• Side $AB$ and $NM$: Marked with one tick (so $AB = NM$).
• Angle at $B$ and angle at $N$: Marked with two ticks (so $\angle B=\angle N$).
• Angle at $Z$ and angle at $L$: Marked with two ticks (so $\angle Z=\angle L$).

Step2: Apply AAS congruence criterion

AAS (Angle - Angle - Side) congruence states that if two angles and a non - included side of one triangle are congruent to the corresponding two angles and non - included side of another triangle, then the triangles are congruent. For $\triangle ABZ$ and $\triangle NLM$:

• $\angle B\cong\angle N$ (given by markings)
• $\angle Z\cong\angle L$ (given by markings)
• $AB\cong NM$ (given by markings, non - included side between the two angles)

By AAS congruence criterion, $\triangle ABZ\cong\triangle NLM$. So the triangles are necessarily congruent.

Answer:

The triangles are necessarily congruent.