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Geometry Arcs and chords

Geometry Arcs and chords. Warm Up. 90° 9. Arcs and Chords. A center angle is an angle whose vertex is the center of a circle. An arc is an unbroken part of a circle consisting of two points called the end points and all the points on the circle between them. A. A. B. B. C. C.

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Geometry Arcs and chords

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  1. GeometryArcs and chords CONFIDENTIAL

  2. Warm Up • 90° • 9 CONFIDENTIAL

  3. Arcs and Chords A center angle is an angle whose vertex is the center of a circle. An arc is an unbroken part of a circle consisting of two points called the end points and all the points on the circle between them. CONFIDENTIAL

  4. A A B B C C Arcs and Their Measure CONFIDENTIAL

  5. A Rock 25% Other 26% M H B Jazz 13% Rap 13% G F Classical 3% C E Pop 13% D R & B 11% Country 10% The circle graph shows the types of music sold during one week at a music store. Find CONFIDENTIAL

  6. Classical 3% Rock 25% Other 26% M H B Jazz 13% Rap 13% G F C E Pop 13% D R & B 11% Country 10% Now you try Use the graph to find each of the following. • 108° • 270° • 36° CONFIDENTIAL

  7. S T R Adjacent arcs are arcs of the same circle that intersect at exactly one point. and are adjacent arcs. CONFIDENTIAL

  8. S T R Arc Addition Postulate The measures of an arc formed by two adjacent arcs is the sum of the measures of the two arcs. CONFIDENTIAL

  9. Using the Arc Addition Postulate CONFIDENTIAL

  10. Now you try! Find each measure. • 140° • 250° CONFIDENTIAL

  11. With in a circle or congruent circles, congruent arcs are two arcs that have the same measure. In the figure, CONFIDENTIAL

  12. CONFIDENTIAL

  13. The converses of the parts of previous theorems are also true. For example, with PART A, congruent chords have congruent central angles CONFIDENTIAL

  14. PART A Proof: CONFIDENTIAL

  15. Applying Congruent Angles, Arcs, and Chords Find each measure. 1) CONFIDENTIAL

  16. 2) CONFIDENTIAL

  17. Now you try! • 12 • 100° Find each measure 1) 2) CONFIDENTIAL

  18. CONFIDENTIAL

  19. Using Radii and Chords CONFIDENTIAL

  20. Now you try! 4) Find QR to the nearest tenth. 4) 46.6 CONFIDENTIAL

  21. Now some problems for you to practice. CONFIDENTIAL

  22. ASSESSMENT 1) The circle graph shows how a typical household spends money on energy. Find each of the following. • 198° • 19.8° • 61.2° • 36 • 39.6 • 324 CONFIDENTIAL

  23. Find each measure. 2) 139° 3) 270° CONFIDENTIAL

  24. 4) 108° 5) 210° CONFIDENTIAL

  25. 6) 24 CONFIDENTIAL

  26. 7) 135° CONFIDENTIAL

  27. REVIEW A A B B C C Arcs and Chords Arcs and Their Measure CONFIDENTIAL

  28. A Rock 25% Other 26% M H B Jazz 13% Rap 13% G F Classical 3% C E Pop 13% D R & B 11% Country 10% The circle graph shows the types of music sold during one week at a music store. Find CONFIDENTIAL

  29. S T R Adjacent arcs are arcs of the same circle that intersect at exactly one point. and are adjacent arcs. CONFIDENTIAL

  30. S T R Arc Addition Postulate The measures of an arc formed by two adjacent arcs is the sum of the measures of the two arcs. CONFIDENTIAL

  31. Using the Arc Addition Postulate CONFIDENTIAL

  32. With in a circle or congruent circles, congruent arcs are two arcs that have the same measure. In the figure, CONFIDENTIAL

  33. CONFIDENTIAL

  34. PART A Proof: CONFIDENTIAL

  35. Applying Congruent Angles, Arcs, and Chords Find each measure. 1) CONFIDENTIAL

  36. 2) CONFIDENTIAL

  37. CONFIDENTIAL

  38. Using Radii and Chords CONFIDENTIAL

  39. You did a great job today! CONFIDENTIAL

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