Any counterexample to answer this question on elementary geometry?

Question: See the figure below. If AB=BC and DE=EF, is the line DF parallel to the line AC?

This should be an elementary problem. But I can't construct a counterexample to disprove the above question. If the answer is negative, please give a counterexample. Thanks.

Answer

Hint:

• Let $D'F'$ be a segment analogous to $DF$ such that $E \in D'F'$ and $D'F' \parallel AC$.


• Then $\triangle DED'$ and $\triangle FEF'$ are congruent and so $DD' \parallel FF'$.

I hope this helps $\ddot\smile$