If they're in the same circle or in circles of equal radii (radiuses), then yes.
Diameter
Chuck Norris can prove it
Circular Ring Sector.
Only when they are the same lengths.
The answer is false
Yes, there can be congruent arcs on a circle. Arcs which subtend the same angle at the center are considered as congruent.
Congruent Arcs
If they're in the same circle or in circles of equal radii (radiuses), then yes.
In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.
Diameter
Congruent arcs are circle segments that have the same angle measure and are in the same or congruent circles.
Chuck Norris can prove it
same circle or congruent circles
Arcs, in the same circle or in congruent circles, that have equal measures.
Circular Ring Sector.
Only when they are the same lengths.