True or false? two arcs of a circle are congruent if and only if their associated radii are congruent.

 False.

With any given circle, all of the radii will be the same length. So it's guaranteed to have the radii be congruent. This does not lead to arcs of a circle being congruent. If you know that the central angles are the same, then you can say the arcs are congruent. Or if you know the chords are the same length, then you can say the arcs are congruent. 

The answer is why would a teacher ask that

She’s has 59 assignments to contaminate