Geometry

Question Analysis:
This question tests the ability to apply the ASA Congruence Postulate when given partial information (two angles) and requires selecting the missing included side to complete the congruence condition.

Key Concept Explanation:
ASA Congruence Postulate states:
If two angles and the included side of one triangle are equal to those of another, the triangles are congruent.

Step-by-Step Solution:
Identify the given angles:
ΔABC has angles ∠A and ∠B.
ΔDEF has angles ∠D and ∠E.
Since ∠A = ∠D and ∠B = ∠E, we already have two angles equal.
Determine the required side for ASA:
For ASA, the side between the two angles must be equal.
In ΔABC, the side between ∠A and ∠B is AB.
In ΔDEF, the side between ∠D and ∠E is DE.
Conclusion:
If AB = DE, then by ASA, ΔABC ≅ ΔDEF.

Option Analysis:
(A) AB = DE ✓ Correct This is the included side between ∠A and ∠B, fulfilling ASA.
(B) BC = EF ✗ Incorrect BC is not between ∠A and ∠B (it’s opposite ∠A). This would fit AAS, not ASA.
(C) AC = DF ✗ Incorrect AC is adjacent to ∠A but not between ∠A and ∠B. This would fit AAS, not ASA.
(D) ∠C = ∠F ✗ Incorrect This would fit AAA, not ASA.

C...