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Section 9-3 Arcs and central angles

Section 9-3 Arcs and central angles. Central angle. An angle with its vertex at the center of the circle. Arcs of circle A. An unbroken part of a circle. Minor arc BC contains the interior points of Major arc BDA contain the remaining points Endpoints of a diameter create a semicircle.

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Section 9-3 Arcs and central angles

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  1. Section 9-3Arcs and central angles

  2. Central angle • An angle with its vertex at the center of the circle.

  3. Arcs of circle A • An unbroken part of a circle. • Minor arc BC contains the interior points of • Major arc BDA contain the remaining points • Endpoints of a diameter create a semicircle

  4. Arcs of Circle A cont..

  5. What do you notice?

  6. Minor arcs • The measure of a minor arc is defined to be the measure of its central angle

  7. What relationship do you notice?

  8. Arc addition postulate • The measure of the arc formed by 2 adjacent arcs is the sum of the measures of these 2 arcs.

  9. Congruent arcs • 2 arcs in the same circle or congruent circles that have the same measure are congruent

  10. Congruent arc theorem • In the same circle, or congruent circles, two minor arcs are congruent if and only if their central angles are congruent

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