Question 479285: Prove that two parallel chords in a circle have congruent arcs.
I need help writing a formal proof to prove this...
Found 2 solutions by solver91311, Edwin McCravy:
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
You cannot prove such a premise in general.
Construct a circle.
Construct a diameter of the circle.
Construct any chord parallel to that diameter.
The diameter is a chord by definition, but has an included arc greater in measure than any lesser chord.
John
My calculator said it, I believe it, that settles it
Answer by Edwin McCravy(20056)  (Show Source):
You can put this solution on YOUR website!
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.
Edwin
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