10.2 Arcs and Chords

1. 10.2 Arcs and Chords Central angle Minor Arc Major Arc

2. Central angle A central angle is an angle which vertex is the center of a circle

3. Minor Arc An Arc is part of the circle. A Minor Arc is an arc above the central angle if the central angle is less then 180°

4. Major Arc A Major Arc is an arc above the central angle if the central angle is greater then 180°

5. Semicircle If the central angle equals 180°, then the arc is a semicircle.

6. Semicircle If the central angle equals 180°, then the arc is a semicircle.

7. Measure of an Arc The measure of an Arc is the same as the central angle.

8. Measure of an Arc The measure of an Arc is the same as the central angle.

9. Postulate: Arc Addition Arcs can be added together.

10. Congruent Arcs If arcs comes from the same or congruent circles, then they are congruent if then have the same measure.

11. Congruent chords Theorem In the same or congruent circles, Congruent arcs are above congruent chords.

12. Theorem If a diameter is perpendicular to a chord , then it bisects the chord and its arc.

13. Theorem If a chord is the perpendicular bisector of another chord (BC), then the chord is a diameter.

14. Solve for y

15. Solve for y

16. Theorem In the same or congruent circles, two chords are congruent if and only if they are an equal distance from the center.

17. Solve for x, QT UV = 6; RS = 3; ST = 3

18. Solve for x, QT UV = 6; RS = 3; ST = 3 x = 4, Since Congruent chord are an equal distance from the center.

19. Solve for x, QT UV = 6; RS = 3; ST = 3 x = 4,

20. Find the measure of the arc Solve for x and y

21. Find the measure of the arc Solve for x and y

22. Homework Page 607 – 608 # 12 - 38

23. Homework Page 608 -609 # 39 – 47, 49 – 51, 69, 76 - 79