Geometry

Question Analysis:
This question involves identifying the correct application of the ASA Congruence Postulate.
The main focus is on determining whether two triangles are congruent using the given angle and side relationships.

Key Concept Explanation:
The ASA (Angle-Side-Angle) Congruence Postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
The included side is the side that is between the two angles.

Step-by-Step Solution:
Review the ASA Congruence Postulate: Two angles and the included side must be given as congruent.
Check each answer choice to see if the information provided fits the ASA rule:
Option A: ∠A ≅ ∠D, ∠B ≅ ∠E, and AC ≅ DF. → Incorrect (Side AC is not between the two given angles.)
Option B: ∠A ≅ ∠D, AB ≅ DE, and ∠C ≅ ∠F. → Incorrect (AB is not between ∠A and ∠C; this follows AAS instead.)
Option C: ∠A ≅ ∠D, AB ≅ DE, and ∠B ≅ ∠E. → Correct (AB is the included side between ∠A and ∠B.)
Option D: AB ≅ DE, BC ≅ EF, and AC ≅ DF. → Incorrect (This follows the SSS Congruence Postulate, not ASA.)

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