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Inscribed Angles Lesson 10.3b

Inscribed Angles Lesson 10.3b. California State Standards. Lesson Goals. Find the measures of arcs and angles within a circle by using the Inscribed Angle Measure Theorem and the Congruent Inscribed Angles Theorem. 4: Prove theorems involving congruence and similarity

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Inscribed Angles Lesson 10.3b

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  1. Inscribed Angles Lesson 10.3b California State Standards Lesson Goals Find the measures of arcs and angles within a circle by using the Inscribed Angle Measure Theorem and the Congruent Inscribed Angles Theorem. • 4: Prove theorems involving congruence and similarity • 7: Prove/use theorems involving circles. • 21: Prove/solve relationships with circles. ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers

  2. definitions • Inscribed Polygon • A polygon with all of its vertices on a circle. • Circumscribe • To circle around something. B C A D P E F

  3. example Find value of x and y. 8xo 8xo 3yo 6yo

  4. theorem Inscribed Right Triangle An inscribed right triangle has a diameter as its hypotenuse. P C Q R

  5. example Find the measure of the arc or angle. B 180o C D A

  6. example Find value of x. B C 3xo A

  7. theorem Inscribed Quadrilateral A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary. P S Q R

  8. example Find value of x and y. S T yo xo 85o 80o R U

  9. example Find value of the measure of each angle. B -10( ) 19yo 19 ( ) A C 10yo 40xo 22xo D

  10. example Find value of the measure of each angle. B 19yo 114o A C 60o 10yo 120o 40xo 66o 22xo D

  11. Today’s Assignment • p.617: 16, 18 – 29 Tribe Pride always my best effort.

  12. Find the value of each variable. Explain. Can the quadrilateral always be inscribed in a circle? Explain your reasoning.

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