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The given image presents two triangles, \(\triangle YXZ\) and \(\triangle NML\), with some angle congruences marked in red. The problem is to determine what additional information is required to prove that the two triangles are congruent using the Angle-Angle-Side (AAS) Postulate.

The AAS Postulate states that if two angles and a non-included side of one triangle are congruent to the corresponding two angles and a non-included side of another triangle, then the two triangles are congruent.

From the image:
- \(\angle Y = \angle N\) (both marked as congruent)
- \(\angle X = \angle M\) (both marked as congruent)

To apply AAS, we need to ensure that a pair of sides, not between the marked angles, are also congruent. Among the given options, **\(\angle Z \cong \angle L\)** completes the required condition for congruence by ensuring the second pair of angles is congruent. This is crucial because, with two angles and one side already being congruent, the triangles can now be confirmed congruent using AAS.

Thus, the correct answer is **\(\angle Z \cong \angle L\)**.

Would you like a deeper explanation on AAS postulate or have any questions?

Here are 5 related questions to deepen your understanding:
1. What is the difference between the AAS and ASA postulates?
2. How does the AAS postulate differ from the SAS postulate?
3. What would be the result if the side between the angles were congruent instead of a non-included side?
4. Could the triangles also be proven congruent using another method besides AAS? If so, how?
5. Why is congruence important in triangle geometry?

**Tip:** When using postulates like AAS, always check if the given information aligns with the required configuration (two angles and a non-included side).

Determine what additional information is required in order to know that the triangles are congruent by AAS Postulate.

Learn how to determine if two triangles are congruent using the AAS (Angle-Angle-Side) Postulate. This example problem demonstrates key geometry concepts involving triangle congruence and the conditions necessary for applying the AAS postulate.

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