Triangles ABC and DEF are congruent by the ASA criterion, as angle A equals angle D, AB equals ED, and AC is parallel to DF.
The property that can be used to show that triangles ABC and DEF are congruent is the Angle-Side-Angle (ASA) criterion. In this case, angle A and angle D are equal (Angle), AB is equal to ED (Side), and AC is parallel to DF, implying that the corresponding angles are congruent (Angle). Therefore, the given information satisfies the conditions of ASA congruence.
The ASA criterion 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 triangles are congruent.
In summary, the congruence of triangles ABC and DEF can be established using the ASA criterion based on the equality of angles A and D, the equality of sides AB and ED, and the parallelism of AC and DF.