Thm: If two chords of a circle are parallel, then the arcs between them are congruent.

A tutoring student asked me if that was a two-way statement (e.g., If arcs between two chords are congruent, then the chords are parallel).

I could not disprove it on the spot, the book did not offer a proof of the theorem.Is it true that if two chords are congruent, then the chords connecting their endpoints are parallel?Prove it! (or disprove it).

If it is true, then why wouldn't the textbook have stated it as an iff statement (I read it very closely, and it wasnotiff).