1. Central Angles and Arc Measures
Advanced Geometry

2. CENTRAL ANGLE
An angle whose vertex is the center of a circle is a central angle.

3. ARC OF A CIRCLE
A section of the circumference of a circle is an arc.

4. MINOR VS MAJOR
MINOR ARC – If the measure of a central angle is less than 180 degrees, then the arc formed by that central angle is a minor arc.
MAJOR ARC – If the measure of a central angle is greater than 180 degrees, then the arc formed by that central angle is a major arc.

5. SEMICIRCLE
If the endpoints of an arc are the endpoints of a diameter, then the arc is a semicircle.

6. Naming Arcs
Minor Arc
Major Arc
Semicircle

7. Example

8. ARC ADDITION POSTULATE
The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs.

9. Measuring Arcs
The measure of a minor arc is defined to be the measure of its central angle.

10. CONGRUENT ARCS
Two arcs of the same circle or of congruent circles are congruent arcs if they have the same measure. central angles are congruent

12. Example

13. Example
Find the measure of arc DE.