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CHAPTER 9: CIRCLES

CHAPTER 9: CIRCLES. 9.5 INSCRIBED ANGLES. INSCRIBED ANGLE. An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. THEOREM 9-7. THEOREM 9-7 The measure of an inscribed angle is equal to half the measure of its intercepted arc. 80 °. 40 °.

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CHAPTER 9: CIRCLES

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  1. CHAPTER 9:CIRCLES 9.5 INSCRIBED ANGLES

  2. INSCRIBED ANGLE An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle.

  3. THEOREM 9-7 THEOREM 9-7 The measure of an inscribed angle is equal to half the measure of its intercepted arc. 80° 40°

  4. PRACTICE y° 130° 100° 50° • Find x. • Find y. • Find z. x° 130° z°

  5. COROLLARY 1 COROLLARY 1 If two inscribed angles intercept the same arc, then the angles are congruent.

  6. EXAMPLE • Find s. • Find t. • 150° • 75° 75° t° s°

  7. COROLLARY 2 COROLLARY 2 An angle inscribed in a semicircle is a right angle.

  8. EXAMPLEIn the image, AC=AB A 180° 90° 90° 180° • Find mCAB • Find mAB • Find mCA • Find m∠CDB C B D

  9. JUST A THOUGHT….. • What is the measure of a circle? • What is mQRS + mSTQ? • What is m∠1? • What is m∠2? • What is m∠1 + m∠2? ½ mQRS + ½ mSTQ = ½ (mQRS + mSTQ) = ½ (360°) = 180° Q R 2 1 S T

  10. COROLLARY 3 COROLLARY 3 If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.

  11. THEOREM 9-8 THEOREM 9-8 The measure of an angle formed by a chord and a tangent is equal to half the measure of the intercepted arc. 150° 210° 75°

  12. CLASSWORK/HOMEWORK 9.5 ASSIGNMENT Classwork: • Pgs. 352-353, Classroom Exercises 2-10 Homework: • Pg. 354, Written Exercises 1-9

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