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Warm up

Warm up. Review HW. Case I: Central Angle: Vertex is AT the center. A. . P. B. Case II: Inscribed Angle: Vertex is ON circle. . ANGLE. ARC. ARC. . ANGLE. 160 . The arc is twice as big as the angle!!. 80 . Find the value of x and y. 120 . . x. . y. . J. K. Q.

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Warm up

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  1. Warm up

  2. Review HW

  3. Case I:Central Angle: Vertex is ATthe center A  P B

  4. Case II:Inscribed Angle: Vertex is ON circle  ANGLE ARC ARC  ANGLE

  5. 160 The arc is twice as big as the angle!! 80

  6. Find the value of x and y 120  x  y 

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

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

  9. If all the vertices of a polygon touch the edge of the circle, the polygon is INSCRIBED and the circle is CIRCUMSCRIBED.

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

  11. If a right triangle is inscribed in a circle then the hypotenuse is the diameter of the circle. diameter

  12. 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

  13. 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?

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

  15. Practice WS Get in your groups please. 12 problems

  16. Homework WS Day 21 Inscribed Angles Choose even or odd problems

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