1. ARCS AND CHORDS Geometry CP1 (Holt 12-2) K.Santos

2. Central Angle Central angle----an angle whose vertex is the center of a circle. A B O < AOB is a central angle

3. Chords and Arcs

4. Arcs and their measures

5. Arcs

6. Adjacent Arcs

7. Arc Addition Postulate 12-2-1

8. Example

9. Theorem 12-2-2 Within a circle or in congruent circles: (1) Congruent central angles have congruent chords (2) Congruent chords have congruent arcs (3) Congruent arcs have congruent central angles

10. Example

11. Theorem 12-2-3

12. Theorem 12-2-4

13. Example Find the value of x. 5 x 5 6 Chords are equidistant from the center so the chords are congruent Bottom chord is 2(6) = 12, so the chord on the right is also 12. Thus, x = 12

14. Example