Question 479285
<pre>
That is false.  As you can see in the circle below, the green 
chord and the red chord are parallel. The green chord subtends the 
green arc and the red chord subtends the red arc, but obviously
the green arc is longer than the red arc, so they cannot be
congruent.  Now, if two chords are congruent, they subtend
congruent arcs, but not necessarily if they are parallel.

{{{drawing(200,200,-5,5,-5,5,

green(arc(0,0,10,-10,36.86989765,143.1301024),line(-4,3,4,3) ),

arc(0,0,10,-10,143.1301024, 233.1301024),

red(arc(0,0,10,-10,233.1301024,306.8698976),line(-3,-4,3,-4)),

arc(0,0,10,-10,306.8698976,36.86989765)



 )}}}

Edwin</pre>