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Chapter 10.2 Notes: Find Arc Measures

Chapter 10.2 Notes: Find Arc Measures. Goal: You will use angle measures to find arc measures. A central angle of a circle is an angle whose vertex is the center of the circle.

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Chapter 10.2 Notes: Find Arc Measures

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  1. Chapter 10.2 Notes: Find Arc Measures Goal: You will use angle measures to find arc measures.

  2. A central angle of a circle is an angle whose vertex is the center of the circle. • If the measure of an angle is less than 180o, then the points on the circle that lie in the interior of the angle form a minor arc. • Minor arcs are named by their endpoints.

  3. The points on the circle that do not lie on the minor arc form a major arc. • A semicircle is an arc with endpoints that are the endpoints of a diameter. • Major arcs and semicircles are named by their endpoints and a point on the arc.

  4. Measuring Arcs • The measure of a minor arc is the measure of its central angle. • The measure of the entire circle is 360o. • The measure of a major arc is the difference between 360o and the measure of the related minor arc. • The measure of a semicircle is 180o.

  5. Ex.1: Find the measure of each arc of where is a diameter. a. b. c. Adjacent Arcs • Two arcs of the same circle are adjacent if they have a common endpoint.

  6. Postulate 23 Arc Addition Postulate: The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs. Ex.2: Identify the given arc as a major arc, minor arc, or semicircle, and find the measure of the arc. a. b. c. d. e. f.

  7. Congruent Circles and Arcs • Two circles are congruent circles if they have the same radius. • Two arcs are congruent arcs if they have the same measure and they are arcs of the same circle or of congruent circles.

  8. Ex.3: Tell whether the red arcs are congruent. Explain why or why not. a. b. c.

  9. Ex.4: Find the measure of each arc of the circle. a. b. c. d. e. f.

  10. Ex.5: Tell whether the red arcs are congruent. Explain why or why not. a. b.

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