10-2 Angles & Arcs

1. 10-2 Angles & Arcs

2. WHO LIKES PIZZA???

3. Angles & Arcs • Arc: an unbroken part of a circle • Minor arc: an arc that is less than a semicircle, or less than 180° (use 2 letters) • Major arc: an arc that is more than a semicircle, or more than 180° (use 3 letters and go the long way) • Semicircle: an arc whose endpoints are the endpoints of the diameter, exactly 180° (use 3 letters to denote which one – there are two)

4. Angles & Arcs • Central Angle: an angle whose vertex is the center of the circle • Intercepted arc: an arc whose endpoints lie on the sides of the angle and whose other points lie in the interior of the angle

5. Arc measures • A Central Angle’s measure is the same as the arc it intercepts. • Arc Measure = Central Angles Measure

6. Inscribed Angles & Arcs • Inscribed angle: an angle whose vertex lies ON a circle and whose sides are chords of the circle (#7)

7. Circles S R T P W Z Y

8. Inscribed angle Theorem(#8) • The measure of the inscribed angle is half the measure of the intercepted arc.

9. Central Angles Sum to 360 • The sum of all central angles in a circle must be 360 degrees

10. Measure and Length • Degree measure of an arc is a portion of the entire circle • Length of the arc is a portion of the circumference or edge of the circle

11. More Angles & Arcs • Degree measure of arcs • The ratio of arc length to circumference is proportional to the ratio of arc measure to 360. • Arc Length *THINK

12. Right Angle Corollary(#10) • If an inscribed angle intercepts a semicircle, then the angle is a right angle

13. Arc-Intercept Corollary(#11) • If 2 inscribed angles intercept the same arc, then they have the same measure

14. The End ~Fin