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Presentation transcript:

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?

C Symbol: C

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

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

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

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

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

Case II: Vertex is ON circle ANGLE ARC ANGLE ARC

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

120 x y Find the value of x and y

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

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

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?

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

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

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

Homework: Page 193 #9-18, Page 207 #1-18