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Warm Up

Warm Up. For each circle C, find the value of x . Assume that segments that appear to be tangent are tangent. 1) 2). Math II. UNIT QUESTION: What special properties are found with the parts of a circle? Standard: MM2G1, MM2G2 Today’s Question:

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Warm Up

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  1. Warm Up For each circle C, find the value of x. Assume that segments that appear to be tangent are tangent. 1) 2)

  2. Math II UNIT QUESTION: What special properties are found with the parts of a circle? Standard: MM2G1, MM2G2 Today’s Question: What is the relationship of an inscribed angle to the measure of its intercepted arc? Standard: MM2G3.b

  3. Inscribed Angle: An angle whose vertex is on the circle and whose sides are chords of the circle INTERCEPTEDARC INSCRIBEDANGLE

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

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

  6. To find the measure of an inscribed angle… 160 80

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

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

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

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

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

  12. A circle can be circumscribed around a quadrilateral if and only if its opposite angles are supplementary. B A D C

  13. Example 8 Find y and z. z 110 110 + y =180 y y = 70 85 z + 85 = 180 z = 95

  14. If a right triangle is inscribed in a circle then the hypotenuse is the diameter of the circle. 180 diameter

  15. Example 6 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

  16. Example 7 In K, m1 = 6x – 5 and m2 = 3x – 4. Find the value of x. 6x – 5 + 3x – 4 = 90 H 2 K x = 11 N 1 G

  17. Classwork: Pg.207 3-7odd 8-15all And 17

  18. Homework: Page 209 1-9 odd 10-17 all 19-24 all

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