arc central angles.pptx powerpoint presentation

Math 10 central arc angles

1. Central Angles and Arcs

2. Central Angles

3. Central angle A central angle is an angle formed by two rays or segment whose vertex is the center of a circle.

4. Central angle Each ray intersects the circle at a point, dividing it into arcs.

5. Sum of Central angles The sum of the measures of the central angles of a circle is 360 degrees. Note: all measures of angles and arcs are in degrees.

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

7. Arcs

8. Arc of a circles an arc is a part of a circle. A semicircle is an arc with a measure equal to one half the circumference of a circle. It is named by using the two endpoints and another endpoint on the arc.

9. Degree Measure of an ARC -The degree measure of a minor arc is the measure of the central angle which intercepts the arc. -The degree measure of a major arc is equal to 360 minus the measure of minor arc with the same endpoints.

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

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

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

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

14. Congruent circles and Congruent arcs

15. Congruent Circles Congruent circles are circles with congruent radii.

16. Congruent Arcs Are arcs of the same circle or of congruent circles with equal measures.

17. Remember: In a circle or in congruent circles, two minor arcs are congruent if and only if their corresponding central angles are congruent.

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

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

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