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Bellwork

Bellwork. Pg 598 1-8. 11.3 Inscribed Angles. Chapter 11 Circles. ). <C is an inscribed angle . AB is the intercepted arc of <C. A. Inscribed Angle. Intercepted Arc. C. B. Theorem 11-9 Inscribed Angle Theorem:

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Bellwork

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  1. Bellwork Pg 598 1-8

  2. 11.3 Inscribed Angles Chapter 11 Circles

  3. ) <C is an inscribed angle. AB is the intercepted arc of <C. A Inscribed Angle Intercepted Arc C B

  4. Theorem 11-9 Inscribed Angle Theorem: The measure of an inscribed angle is half the measure of its intercepted arc. m<B = ½ mAC ) A B C

  5. a° ) m<PQT = ½ mPT P Find the values of a and b. 60 = ½ a T a = 120° 30° S ) m<PRT = ½ PS 60° b = ½ (a + 30) Q b = ½ (120 + 30) 60° b° b = ½ (150) b = 75 R ) Find m<PQR if mRS = 60 m<PQR = ½ ( a + 30 + 60) m<PQR = ½ (120 + 30 + 60) m<PQR = ½ (210) m<PQR = 105°

  6. Corollaries to the Inscribed Angle Theorem: • Two inscribed angles that intercept the same arc are congruent. • An angle inscribed in a semicircle is a right angle. • The opposite angles of a quadrilateral inscribed in a circle are supplementary.

  7. 40° <1 is 90° because it is inscribed in a semicircle (180°) Find the measure of the numbered angle. 70° 1 <2 and the 38° intercept the same arc, so the angles are congruent. m<2 = 38° 70° 2 38°

  8. Find the measure of each numbered angle. m<1 = 90° 1 m<3 = 90° m<4 = ½ (80 + 60) 80° 4 m<4 = 70° m<2 = 180 - 70 m<2 = 110° 2 3 60°

  9. Theorem 11-10 The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc m<C = ½ mBDC ) B B D D C C

  10. In the diagram, KJ is tangent to the circle at J. Find the values of x and y. ) x = ½ mJL ) ½ mJL = <Q ) J Q ½ mJL = 35° 35° x = 35° x° ) y° y = ½ QJ QJ = 180 - 70 L QJ = 110° y = ½ (110) K y = 55°

  11. Homework: pg 601 2 – 24 even

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