Answer:
Choice C.
Step-by-step explanation:
If the triangles ABC and EDC are similar, then their interior angles are congruent.
This, for example, means that angle A is congruent to angle E.
That in turn means that the angle the line AB makes with AE is the same as the angle line ED makes with AE.
Since the angles are equal, this implies that the lines AE and DE can never intersect, and therefore, must be parrallel.