Section 9-3

1. Section 9-3 Arcs and Central Angles

2. Circle B is a central angle Central angle • An angle with its vertex at the center of a circle.

3. ARC • an unbroken part of a circle : read “arc AC”

4. Types of Arcs: • Minor Arc: less than 180 • Measure is the same as its central angle • Named using two letters (Ex: ) 2. Major Arc: more than 180 • Measure is 360 minus the measure of its central angle • Named using three letters (Ex: ) 3. Semicircle: equals 180 • Endpoints of a diameter • Named using three letters

5. and Adjacent Arcs • Arcs in a circle that have exactly one point in common. are adjacent arcs

6. Arc addition postulate • The measure of the arc formed by two adjacent arcs is the sum of the measures of these two arcs. • Applies like segment addition postulate

7. ABD

8. Congruent Arcs • Arcs, in the same circle or in congruent circles, that have equal measures.

9. Theorem 9-3 • In the same circle or in congruent circles, two minor arcs are congruent if and only if their central angles are congruent.