1. Arcs and Chords lesson 10.2a California State Standards 4: Prove theorems involving congruence and similarity 7: Prove/use theorems involving circles. 21: Prove/solve relationships with circles. Lesson Goals Find the measure of arcs in a circle using the definition of arc measure and the arc addition postulate. 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 180 o The measure of an minor arc equals the measure of its central angle.

3. definitions C A B

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

5. definitions C A B D

6. C P Q

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

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

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

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

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

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

13. 13 Today’s Assignment  p. 607: 12 – 38

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