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

angle J K L approximately equal to angle F L K

top enclose F K end enclose approximately equal to top enclose L J end enclose

top enclose F K end enclose approximately equal to top enclose J K end enclose

top enclose F L end enclose approximately equal to top enclose K J end enclose

To determine if the triangles \( \triangle FKL \) and \( \triangle JKL \) are congruent by the **AAS Postulate** (Angle-Angle-Side), we need the following:

### AAS Postulate states:
Two triangles are congruent if **two angles** and the **non-included side** in one triangle are respectively equal to two angles and the corresponding non-included side in another triangle.

In the diagram, you already have the following information:
1. **Angle \( \angle JKL \) is approximately equal to angle \( \angle FLK \)** (this is one pair of angles).
2. **Side \( \overline{KL} \)** is a common side to both triangles \( \triangle FKL \) and \( \triangle JKL \).

### What is missing?
To use the **AAS Postulate**, you need to know one more angle in each triangle. From the choices given, we need:
- **\( \angle FK \approx \angle JK \)** (This would give two angles in each triangle and the side \( KL \) as the non-included side).

Thus, the correct additional information needed would be:  
**\( \angle FK \approx \angle JK \)** (3rd option in your list).

Would you like more details on how congruence postulates work or have any further questions?

### Related questions:
1. What is the difference between AAS and ASA postulates?
2. How can you identify corresponding parts of congruent triangles?
3. Why is the non-included side important in the AAS postulate?
4. How does knowing that \( KL \) is a shared side help with triangle congruence?
5. Can you apply the AAS postulate without knowing the lengths of the sides?

### Tip:
When using the AAS Postulate, always ensure that the side you are comparing is not between the two given angles; otherwise, you are applying the ASA postulate instead.

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

Learn what additional information is needed to prove triangle congruence by the AAS Postulate. This problem involves understanding the Angle-Angle-Side theorem and applying it to triangles in geometry. Suitable for students in Grades 8-10.

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