1. 1.Name 2.Who can you help you learn the best in class? 3.Who can you NOT work with in class? 4.Where do you want to sit?

2. C Symbol: C

5. Math II UNIT QUESTION: What special properties are found with the parts of a circle? Standard: MM2G1, MM2G2 Today’s Question: How are central angles different from inscribed angles? Standard: MM2G3.b

6. P A B C Case I: Vertex is AT the center

7. P E F D Semicircle: An Arc that equals 180° EDF To name: use 3 letters

8. P A B C Minor ArcMajor Arc Less than 180° More than 180° AB ACB Central Angle : vertex is at the center of the circle

9. measure of an arc = measure of central angle A B C Q 96  m AB m ACB m AE E = = = 2x + 14 Find x. 96° 264° x = 35

10. Case II: Vertex is ON circle ANGLE ARC ANGLE ARC

11. 160  80  The arc is twice as big as the angle!!

12. 120 x y Find the value of x and y

13. Examples 1. If m JK = 80  and  JMK = 2x – 4, find x. M Q K S J 2. If m  MKS = 56 , find m MS. x = 22 112 

14. 72˚ If two inscribed angles intercept the same arc, then they are congruent. Find the measure of  DOG and  DIG D O G I

15. Example 3 In  J, m  3 = 5x and m  4 = 2x + 9. Find the value of x. 3 Q D J T U 4 x = 3

16. H K G N 4x – 14 = 90 Example 4 In  K, GH is a diameter and m  GNH = 4x – 14. Find the value of x. x = 26 Bonus: What type of triangle is this? Why?

17. Classwork Workbook Page 204 #12-24 Workbook Page 218 & 219

18. a quadrilateral inscribed in a circle: opposite angles are supplementary. A B C D

19. z y 110 85 110 + y =180 y = 70 z + 85 = 180 z = 95 Example 5 Find y and z.

20. Homework: Page 193 #9-18, 21-27 Page 207 #1-18