Section 9-3 Arcs and Central Angles

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

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

Types of Arcs: 1.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

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

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

ABD

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

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.