The definition of arpeggio necessitates chord tones. Arpeggio = broken chord (chord broken into single notes).
About the chord theory - the OP, HonketyHank, made a neat little video about this a while back for The Woodshed Study Group here -- a video by a newbie, for newbies -- that explains this graphically. Give him some love by checking it out:
https://www.youtube.com/watch?v=7fQnBhl9TUo
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