1. Arcs of a Circle

2. The Circle and their Arcs
An arc consists of two points on a circle and all of the points on the circle needed to connect the points by a single path

3. The Circle and their Arcs
Center of an ARC
The center of an arc is the center of the circle of which the arc is a part.

4. The Circle and their Arcs
Central Angle
A central angle is an angle whose vertex is at the center of a circle.
The measure of a central angle is equal to the measure of it’s intercepted arc!
63 degrees
131 degrees ?
Note: the measure of a central angle is less than 180 degrees

5. The Circle and their Arcs
Minor ARC
A minor arc is an arc whose points are on or between the sides of a central angle
The measure of a minor arc is always less than 180 degrees
A minor arc is named with its endpoints.

6. The Circle and their Arcs
Major ARC
A major arc is an arc whose points are outside the sides of a central angle
The measure of a major arc is always greater than 180 degrees
A major arc must be named with three points on the circle!

7. The Circle and their Arcs
Semicircle
A semicircle is an arc whose endpoints are on the diameter of a circle
The measure of a semicircle is always equal to 180 degrees
A semicircle must be named with three points on the circle!

8. The Circle and their Arcs
Measure of a Minor ARC
The measure of a minor arc is equal to the measure of its central angle
The measure of a minor arc is always less than 180 degrees
The measure of the minor arc is indicated by

9. The Circle and their Arcs
Measure of a Major ARC
The measure of a major arc is equal to the 360 minus the measure of its central angle
The measure of a minor arc is always more than 180 degrees
The measure of the major arc is indicated by

10. The Circle and their Arcs
Congruent Arcs
Two arcs are congruent whenever they have the same measure and are parts of the same circle or congruent circles.

11. The Circle and their Arcs
Arcs with the same measure that are NOT Congruent Arcs
3cm
5 cm
Arcs are not in the same or congruent circles!