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Math II Unit: Circle Properties

Explore central and inscribed angles, semicircles, major and minor arcs in circles. Practice solving angles and arc measures. Learn about special properties in circles and quadrilaterals inscribed in circles.

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Math II Unit: Circle Properties

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  1. Seat/Partner • Name • Who can you help you learn the best in class? • Who can you NOT work with in class? • Where do you want to sit?

  2. C C Symbol:

  3. Unit 3A Circles

  4. Assignment on Blog

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

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

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

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

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

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

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

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

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

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

  16. Example 4 In K, GH is a diameter and mGNH = 4x – 14. Find the value of x. 4x – 14 = 90 H K x = 26 N G 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. B A D C

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

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

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