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Understanding Arcs and Central Angles in Circles

Explore different types of arcs, including minor and major arcs, semicircles, and adjacent arcs. Learn about the Arc Addition Postulate, Congruent Arcs, and Theorem 9-3.

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Understanding Arcs and Central Angles in Circles

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  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.

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