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The question is asking about the conditions under which two triangles \( \triangle ABC \) and \( \triangle DEF \) will be congruent by the SAS (Side-Angle-Side) axiom. The information given is:

- \( AB = FD \)
- \( \angle A = \angle D \)

For two triangles to be congruent by the SAS (Side-Angle-Side) axiom, two sides and the included angle between those sides in one triangle must be equal to the corresponding two sides and the included angle in the other triangle.

Given:
- \( AB = FD \) (Side)
- \( \angle A = \angle D \) (Angle)

For the SAS condition to hold, we need the second pair of sides that include \( \angle A \) and \( \angle D \) to be equal, i.e., \( AC = DE \).

So, the triangles will be congruent by the SAS axiom if \( AC = DE \).

Would you like to go over more details or have any questions? Here are some related questions:

1. What is the significance of the SAS axiom in proving triangle congruence?
2. How does the SAS axiom differ from the SSS and ASA axioms?
3. What would happen if the non-included side was equal instead of the included one?
4. How can you use the SAS axiom to solve for unknown sides or angles in triangles?
5. Why is it important that the angle be included between the two sides in the SAS axiom?

**Tip:** Remember that in the SAS axiom, the angle must be between the two sides for the congruence to be valid.

In triangles ABC and DEF, AB = FD and ∠A = ∠D. The two triangles will be congruent by SAS axiom if _____?

Understand how triangles ABC and DEF are congruent using the SAS (Side-Angle-Side) axiom. This problem explores conditions for triangle congruence, including equal sides and angles, suitable for students in Grades 8-10.

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