Answer:
The arcs of the circle are congruent.
If you've ever drawn a circle, you know that a circle is formed when two straight lines intersect in the interior of a circle. We know that when two lines intersect, they form a line segment with endpoints. This line segment is the same length as the radius of the circle. If we look at the picture below, we can see that the endpoints of the radius of the circle form a line segment.
This line segment is the same length as the radius of the circle.
The lines above are parallel, so the line segment they form is perpendicular to both lines and they touch both lines at the same point. This point is both the beginning and ending of the line segment. Therefore, the line segment produced by the intersection of two parallel lines is a perpendicular to those lines. We can also call this perpendicular a radius of the circle.
The lines intersecting the circle at a 90-degree angle form a chord. And if we draw a chord across the diameter of the circle and along the chord, we see that these chords form a rectangle. This rectangle can be called the inscribed rectangle, or the sector. The complete segment formed by the chord and the sector is the arc of the circle.
Therefore, the arcs of the circle are congruent to the sector. Here, we can see that the arcs of the circle are congruent. We can't represent the relationship of congruency in this diagram because we need to pull the lines in this diagram closer together in order to see it in a way that does not distort the shape of the sector and arcs of the circle. But it seems that the segments are congruent to the sector.
After all, the lines in a circle with a radius of x are parallel.
