Geometry Section 10-3 1112

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Arcs and Chords

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Geometry Section 10-3 1112

  1. 1. Section 10-3 Arcs and ChordsMonday, May 14, 2012
  2. 2. Essential Questions • How do you recognize and use relationships between arcs and chords? • How do you recognize and use relationships between arcs, chords, and diameters?Monday, May 14, 2012
  3. 3. Theorems 10.2 - Congruent Minor Arcs: 10.3 - Perpendicularity: 10.4 - Perpendicularity: 10.5 - Congruent Chords:Monday, May 14, 2012
  4. 4. Theorems 10.2 - Congruent Minor Arcs: In the same or congruent circles, two minor arcs are congruent IFF their corresponding chords are congruent 10.3 - Perpendicularity: 10.4 - Perpendicularity: 10.5 - Congruent Chords:Monday, May 14, 2012
  5. 5. Theorems 10.2 - Congruent Minor Arcs: In the same or congruent circles, two minor arcs are congruent IFF their corresponding chords are congruent 10.3 - Perpendicularity: If a diameter or radius of a circle is perpendicular to a chord, then it bisects the chord and its arc 10.4 - Perpendicularity: 10.5 - Congruent Chords:Monday, May 14, 2012
  6. 6. Theorems 10.2 - Congruent Minor Arcs: In the same or congruent circles, two minor arcs are congruent IFF their corresponding chords are congruent 10.3 - Perpendicularity: If a diameter or radius of a circle is perpendicular to a chord, then it bisects the chord and its arc 10.4 - Perpendicularity: The perpendicular bisector of a chord is a diameter or radius of the circle 10.5 - Congruent Chords:Monday, May 14, 2012
  7. 7. Theorems 10.2 - Congruent Minor Arcs: In the same or congruent circles, two minor arcs are congruent IFF their corresponding chords are congruent 10.3 - Perpendicularity: If a diameter or radius of a circle is perpendicular to a chord, then it bisects the chord and its arc 10.4 - Perpendicularity: The perpendicular bisector of a chord is a diameter or radius of the circle 10.5 - Congruent Chords: In the same or congruent circles, two chords are congruent IFF they are equidistant from the centerMonday, May 14, 2012
  8. 8. Example 1  = 90°. Find mAB. In  X, AB ≅ CD and mCD Monday, May 14, 2012
  9. 9. Example 1  = 90°. Find mAB. In  X, AB ≅ CD and mCD   = 90° mABMonday, May 14, 2012
  10. 10. Example 2  ≅ YZ . Find WX. In the figure,  A ≅ B and WX Monday, May 14, 2012
  11. 11. Example 2  ≅ YZ . Find WX. In the figure,  A ≅ B and WX  7x − 2 = 5x + 6Monday, May 14, 2012
  12. 12. Example 2  ≅ YZ . Find WX. In the figure,  A ≅ B and WX  7x − 2 = 5x + 6 2x = 8Monday, May 14, 2012
  13. 13. Example 2  ≅ YZ . Find WX. In the figure,  A ≅ B and WX  7x − 2 = 5x + 6 2x = 8 x=4Monday, May 14, 2012
  14. 14. Example 2  ≅ YZ . Find WX. In the figure,  A ≅ B and WX  7x − 2 = 5x + 6 2x = 8 x=4 WX = 7(4) − 2Monday, May 14, 2012
  15. 15. Example 2  ≅ YZ . Find WX. In the figure,  A ≅ B and WX  7x − 2 = 5x + 6 2x = 8 x=4 WX = 7(4) − 2 WX = 28 − 2Monday, May 14, 2012
  16. 16. Example 2  ≅ YZ . Find WX. In the figure,  A ≅ B and WX  7x − 2 = 5x + 6 2x = 8 x=4 WX = 7(4) − 2 WX = 28 − 2 WX = 26Monday, May 14, 2012
  17. 17. Example 3  =150°. Find mDE. In  G, mDEF Monday, May 14, 2012
  18. 18. Example 3  =150°. Find mDE. In  G, mDEF   = 1 mDEF mDE  2Monday, May 14, 2012
  19. 19. Example 3  =150°. Find mDE. In  G, mDEF   = 1 mDEF mDE  2  = 1 (150) mDE 2Monday, May 14, 2012
  20. 20. Example 3  =150°. Find mDE. In  G, mDEF   = 1 mDEF mDE  2  = 1 (150) mDE 2  = 75° mDEMonday, May 14, 2012
  21. 21. Example 4 In  C, AB =18 inches and EF = 8 inches. Find CD.Monday, May 14, 2012
  22. 22. Example 4 In  C, AB =18 inches and EF = 8 inches. Find CD. CF is a radius.Monday, May 14, 2012
  23. 23. Example 4 In  C, AB =18 inches and EF = 8 inches. Find CD. CF is a radius. a +b =c 2 2 2Monday, May 14, 2012
  24. 24. Example 4 In  C, AB =18 inches and EF = 8 inches. Find CD. CF is a radius. a +b =c 2 2 2 4 +b =9 2 2 2Monday, May 14, 2012
  25. 25. Example 4 In  C, AB =18 inches and EF = 8 inches. Find CD. CF is a radius. a +b =c 2 2 2 4 +b =9 2 2 2 16 + b = 81 2Monday, May 14, 2012
  26. 26. Example 4 In  C, AB =18 inches and EF = 8 inches. Find CD. CF is a radius. a +b =c 2 2 2 4 +b =9 2 2 2 16 + b = 81 2 b = 65 2Monday, May 14, 2012
  27. 27. Example 4 In  C, AB =18 inches and EF = 8 inches. Find CD. CF is a radius. a +b =c 2 2 2 4 +b =9 2 2 2 16 + b = 81 2 b = 65 2 b = 65Monday, May 14, 2012
  28. 28. Example 4 In  C, AB =18 inches and EF = 8 inches. Find CD. CF is a radius. a +b =c 2 2 2 4 +b =9 2 2 2 16 + b = 81 2 b = 65 2 b = 65 inches or ≈ 8.06 inchesMonday, May 14, 2012
  29. 29. Example 5 In  P, EF = GH = 24, PQ = 4x − 3, and PR = 2x + 3. Find PQ.Monday, May 14, 2012
  30. 30. Example 5 In  P, EF = GH = 24, PQ = 4x − 3, and PR = 2x + 3. Find PQ. 4x − 3 = 2x + 3Monday, May 14, 2012
  31. 31. Example 5 In  P, EF = GH = 24, PQ = 4x − 3, and PR = 2x + 3. Find PQ. 4x − 3 = 2x + 3 2x = 6Monday, May 14, 2012
  32. 32. Example 5 In  P, EF = GH = 24, PQ = 4x − 3, and PR = 2x + 3. Find PQ. 4x − 3 = 2x + 3 2x = 6 x=3Monday, May 14, 2012
  33. 33. Example 5 In  P, EF = GH = 24, PQ = 4x − 3, and PR = 2x + 3. Find PQ. 4x − 3 = 2x + 3 2x = 6 x=3 PQ = 4(3) − 3Monday, May 14, 2012
  34. 34. Example 5 In  P, EF = GH = 24, PQ = 4x − 3, and PR = 2x + 3. Find PQ. 4x − 3 = 2x + 3 2x = 6 x=3 PQ = 4(3) − 3 PQ = 12 − 3Monday, May 14, 2012
  35. 35. Example 5 In  P, EF = GH = 24, PQ = 4x − 3, and PR = 2x + 3. Find PQ. 4x − 3 = 2x + 3 2x = 6 x=3 PQ = 4(3) − 3 PQ = 12 − 3 PQ = 9Monday, May 14, 2012
  36. 36. Check Your Understanding p. 704 #1 - 6Monday, May 14, 2012
  37. 37. Problem SetMonday, May 14, 2012
  38. 38. Problem Set p. 705 #7-33 odd, 45, 49, 51 "I may not have gone where I intended to go, but I think I have ended up where I needed to be." - Douglas AdamsMonday, May 14, 2012

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