When two arcs are parallel to each other, the two arcs between them are congruent. If the two arcs they intersect are the same length, they are congruent.
Chords within a circle can be related in a variety of ways. Parallel chords cut congruent arcs in the same circle. That is, the arcs whose endpoints include one of each chord's endpoints have equal measures.
The lengths of the arcs connecting two parallel chords of a circle are equal. Similarly, if the lengths of the two arcs connecting two distinct chords are the same, the chords are parallel. If two chords have the same length, the arcs between their endpoints will have the same measure.
When two arcs are parallel to each other, the two arcs between them are congruent. If the two arcs they intersect are the same length, they are congruent.
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