We know that when the chords are congruent, the arcs that they correspond to are congruent as well.
Work Step by Step
A circle is uniform throughout, and congruent chords are the same length. Thus, let us consider taking a chord and placing it wherever on the circle that we wish. Since the chords are congruent and the circle is symmetric, this will intersect the circle in exactly the same way no matter where we put the chord. If it intersects the circle in the same way, this means that the arcs must be congruent.