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Understanding Arcs and Central Angles in Circles

Explore the concept of central angles and arcs in circles, including minor arcs, major arcs, and semicircles. Learn about adjacent arcs, the arc addition postulate, and congruent arcs.

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Understanding Arcs and Central Angles in Circles

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  1. Section 10-2 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. Named using two letters • (Ex: ) Three Types of Arcs: • Minor Arc: less than • Measure is the same as • its central angle

  5. 2. Major Arc: more than • Named using three letters (Ex: ) • Measure is 360 minus the measure of its associated minor arc

  6. 3.Semicircle: equals • Endpoints of the arc are the endpoints of a diameter • Named using three letters

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

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

  9. ABD

  10. Congruent Arcs • Two arcs of the same circle or of congruent circles are congruent if they have the same measure.

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