Arcs:

An arc is an unbroken part of a circle.

Consider the circle:

If EF is the diameter then the arcs formed are semi circles.

The arc EF called a minor arc is formed by the interior ÐECF and the points on the between point E and F.

The remaining part of C and points E and F is called the major arc, denoted as EGF. Major arcs and semicircles are named with three points on the circle.

 

The central angle of a circle is an angle with its vertex at the center of the circle. The central angle of an arc is the central angle of a circle with the endpoints of the angle intersects a minor arc.
The central angle of is ÐECF.

The measure of a minor arc is the measure of its central angle.

The measure of a semicircle will always be 180°, and the measure of major arcs will always be larger than 180°.

Arcs having a single common point are adjacent non overlapping arcs.

Postulate: Arc Addition Postulate.

The measure of the arc formed by two non overlapping adjacent arcs is the sum of the measures of their central angles.

Theorem:

In congruent circles or in the same circle, two minor arcs are congruent if and only if their central angles are congruent.