2. P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than 180° More than 180° AB ACB To name: use 2 letters To name: use 3 letters <APB is a Central Angle

3. P E F D Semicircle: An Arc that equals 180° EDF To name: use 3 letters EF is a diameter, so every diameter divides the circle in half, which divides it into arcs of 180°

4. THINGS TO KNOW AND REMEMBER ALWAYS A circle has 360 degrees A semicircle has 180 degrees Vertical Angles are Equal Linear Pairs are Supplementary

5. Vertical Angles are Equal

6. Linear Pairs are Supplementary http://www.mathopenref.com/linearpair.html 120°60°

7. measure of an arc = measure of central angle A B C Q 96  m AB m ACB m AE E = = = 96° 264° 84°

8. Arc Addition Postulate A B C m ABC = m AB + m BC

9. Tell me the measure of the following arcs. 80  100  40  140  A B C D R m DAB = m BCA = 240  260 

10. Congruent Arcs have the same measure and MUST come from the same circle or from congruent circles. 45 A B C D 110

11. Classwork Page 193 #9-18 You have 15 minutes.

12. Inscribed Angle: An angle whose vertex is on the circle and whose sides are chords of the circle INSCRIBED ANGLE INTERCEPTED ARC

13. Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle. C L O T 1. YES; CL

14. Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle. Q R K V 2. NO; QVR S

15. 160° 80° To find the measure of an inscribed angle…

16. http://www.geogebra.org /en/upload/files/english/ Guy/Circles_and_angles/ Inscribed_Anlge.html

17. 120 x What do we call this type of angle? What is the value of x? y What do we call this type of angle?How do we solve for y? The measure of the inscribed angle is HALF the measure of the inscribed arc!!

18. http://www.geogebra.org/en/upload/fi les/english/Guy/Circles_and_angles/I nscribed_angle_practice.html

19. Examples 3. If m JK = 80 , find m <JMK. M Q K S J 4. If m <MKS = 56 , find m MS. 40  112 

20. 72  If two inscribed angles intercept the same arc, then they are congruent.

21. http://www.geogebra.org/en/upload /files/english/Guy/Circles_and_ang les/Inscribed_angle_practice.html

22. Example 5 In  J, m< A= 5x and m< B = 2x + 9. Find the value of x. A Q D J T U B m<A = m<B 5x = 2x+9 x = 3

23. Classwork: Page 193 #9-23 Page 207 #1-15

24. Whatever is left is homework