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Arcs and Chords lesson 10.2a

Arcs and Chords lesson 10.2a. California State Standards. Lesson Goals. Find the measure of arcs in a circle using the definition of arc measure and the arc addition postulate. 4: Prove theorems involving congruence and similarity 7: Prove/use theorems involving circles.

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Arcs and Chords lesson 10.2a

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  1. Arcs and Chords lesson 10.2a California State Standards Lesson Goals Find the measure of arcs in a circle using the definition of arc measure and the arc addition postulate. 4: Prove theorems involving congruence and similarity 7: Prove/use theorems involving circles. 21: Prove/solve relationships with circles. ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers

  2. definitions • Central Angle • An angle whose vertex is the center of a circle. • Minor Arc • A section of the circle cut by a central angle that measures less than 180o • The measure of an minor arc equals the measure of its central angle.

  3. minor arc A definitions central angle C B

  4. definitions • Major Arc • A section of the circle that measures more than 180o. • The measure of a major arc equals the difference between 360o and the measure of its associated minor arc. • Semicircle • An arc with endpoints coinciding with the endpoints of a diameter

  5. major arc A definitions C B D

  6. semicircle definitions P C Q

  7. example Find the measure of each arc. 32o E 328o C 148o 180o H I

  8. example Find the measure of each arc. 142o S D 118o 60o 82o C 218o 100o T E

  9. definitions Congruent Arcs Arcs with the same measure within the same circle or congruent circles. E A because C D B

  10. You try Find the measure of each arc. B 70o A 70o 110o D C E

  11. example Find the measure of each arc. A 150o B 150o C 210o Yes D E

  12. example Find the measure of each arc. 36o 36o 144o

  13. Today’s Assignment • p. 607: 12 – 38 Tribe Pride always my best effort.

  14. and are diameters. COPY the diagram. Find the indicated measure. Determine whether the arc is a minor arc, a major arc, or a semicircle of circle R. Find the measure of the red arc. Use circle P to find the value ofx. Then find the measure of the red arc. 35. Name 2 pairs of congruent arcs in #32 – 34. Explain your reasoning.

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