Final answer:
Congruent central angles in a circle determine congruent minor arcs, which are arcs with the same length and degree measure.
Step-by-step explanation:
Congruent central angles in a circle will always determine congruent minor arcs. These arcs are the portions of the circle that lie inside the central angles. Since the central angles are congruent, the corresponding arcs must span the same length, regardless of the size of the circle. This is because the central angle of a circle is directly proportional to the arc that it intercepts. Therefore, if two central angles are equal, the intercepted arcs must also be equal in length.
In more than 100 words, if we have a circle and two central angles that are congruent, the arcs that they intercept on the circumference will also be congruent. This means that each arc will have the same degree measure and the same arc length, provided the arcs are of the same circle. For instance, if both central angles measure 60 degrees, each of the corresponding arcs will also represent 60 degrees of the 360-degree total circumference of a circle, determining congruent minor arcs.