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Lesson 9.4 Inscribed Angles pp. 390-393

Lesson 9.4 Inscribed Angles pp. 390-393. Objectives: 1. To identify and prove theorems relating inscribed angles to the measure of their intercepted arcs. 2. To state other relationships that involve inscribed angles. Theorem 9.13

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Lesson 9.4 Inscribed Angles pp. 390-393

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  1. Lesson 9.4 Inscribed Angles pp. 390-393

  2. Objectives: 1. To identify and prove theorems relating inscribed angles to the measure of their intercepted arcs. 2. To state other relationships that involve inscribed angles.

  3. Theorem 9.13 The measure of an inscribed angle is equal to one-half the measure of its intercepted arc.

  4. A K C B

  5. A K B D C

  6. A C B D K

  7. B O C A If mAC = 60, then mABC = 30.

  8. Theorem 9.14 If two inscribed angles intercept congruent arcs, then the angles are congruent.

  9. B O D C A ABC  ADC

  10. Theorem 9.15 An angle inscribed in a semicircle is a right angle.

  11. O A C B mABC = 90.

  12. Theorem 9.16 The opposite angles of an inscribed quadrilateral are supplementary.

  13. D O A C B ABC and ADC are supplementary. BAD and BCD are supplementary.

  14. Given: In circle M, mRT = 80, mSQ = 64. Find mQTS. R Q U M T S P

  15. Given: In circle M, mRT = 80, mSQ = 64. Find mTQR. R Q U M T S P

  16. Given: In circle M, mRT = 80, mSQ = 64. Find mTQP. R Q U M T S P

  17. Given: In circle M, mRT = 80, mSQ = 64. Find mTPR. R Q U M T S P

  18. A B K D C E Given: In circle K, AB || DE, AC  BC; mBAC = 56°. Find mAC.

  19. A B K D C E Given: In circle K, AB || DE, AC  BC; mBAC = 56°. Find mBC.

  20. A B K D C E Given: In circle K, AB || DE, AC  BC; mBAC = 56°. Find mACB.

  21. A B K D C E Given: In circle K, AB || DE, AC  BC; mBAC = 56°. Find mABC.

  22. A B K D C E Given: In circle K, AB || DE, AC  BC; mBAC = 56°. Find mAB.

  23. Homework pp. 392-393

  24. ►A. Exercises 1. If mDC = 60°, find m4. D C X 1 2 3 4 O A B

  25. ►A. Exercises 3. If m3 = 25°, find mDC. D C X 1 2 3 4 O A B

  26. D C X 1 2 3 4 O A B ►A. Exercises 5. If m3 = 28°, find m4.

  27. ►A. Exercises 7. If mDC = 55°, find mDBC. D C X 1 2 3 4 O A B

  28. ►A. Exercises 9. If mADB = 290°, find m1. D C X 1 2 3 4 O A B

  29. ►B. Exercises 11. If mDC = 68° and mAB = 134°, find mDXA. D C X 1 2 3 4 O A B

  30. ►B. Exercises Use the following figure for exercises 12-16. 13. If mMLO = 240°, find mMLO. M L P Y N O

  31. ►B. Exercises Use the following figure for exercises 12-16. 15. If mMLO = 212°, find mMNO and mMLO. M L P Y N O

  32. ■ Cumulative Review Justify each statement with a reason. Given: ABC is obtuse; CD  AB at D E C A D B 27. CDA and CDB are right angles.

  33. ■ Cumulative Review Justify each statement with a reason. Given: ABC is obtuse; CD  AB at D E C A D B 28. BC  BD

  34. ■ Cumulative Review Justify each statement with a reason. Given: ABC is obtuse; CD  AB at D E C A D B 29. mACE = mB + mCAD

  35. ■ Cumulative Review Justify each statement with a reason. Given: ABC is obtuse; CD  AB at D E C A D B 30. AE + AB  BE

  36. ■ Cumulative Review Justify each statement with a reason. Given: ABC is obtuse; CD  AB at D E C A D B 31. mBAE + mABE + mE = 180°

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