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横截线与平行线相交探究

横截线与平行线相交探究
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2017-09-27 05:33
角几何作图
①本范例演示横截线与平行线相交时形成的特殊角对关系；②涉及核心数学概念包括角、平行线性质、同位角、内错角、同旁内角等；③作图要点运用了Point, Circle, Intersect, Rotate, Angle, Line, Ray, Segment, CircleSector等GeoGebra命令与对象；④适合初中及以上数学教学，用于帮助学生直观理解平行线与横截线间的角度关系，培养空间想象能力。

GeoGebra 命令及参数

  1. Point(f) → A
  2. Circle(A, 2) → c
  3. Intersect(c, f, 2) → B
  4. Rotate(B, (a * π / 180), A) → B'
  5. Rotate(f, (b * π / 180), A) → f'
  6. Intersect(c, f', 2) → F
  7. Rotate(F, (a * π / 180), A) → F'
  8. Angle(F, A, F') → α
  9. Line(A, F') → g
  10. Intersect(c, g, 1) → C
  11. Ray(A, F') → h
  12. Ray(A, C) → i
  13. Intersect(c, f', 1) → D
  14. Ray(A, F) → j
  15. Ray(A, C) → k
  16. Ray(A, D) → l
  17. Point(l) → E
  18. Point(h) → G
  19. Point(k) → H
  20. Point(j) → I
  21. Line(G, j) → m
  22. Circle(G, 1) → d
  23. Intersect(d, m) → J, K
  24. Intersect(d, h) → L, M
  25. Ray(G, K) → n
  26. Ray(G, J) → p
  27. Point(n) → O
  28. Point(p) → P
  29. Intersect(d, h, 2) → Q
  30. Ray(G, Q) → q
  31. Segment(A, G) → r
  32. Point(q) → N
  33. Circle(G, 1.5) → c_1
  34. Circle(A, 1.5) → d_1
  35. Intersect(c_1, n, 1) → R
  36. Intersect(c_1, q, 1) → S
  37. Intersect(c_1, p, 1) → T
  38. Intersect(c_1, r, 1) → U
  39. Intersect(d_1, j, 1) → V
  40. Intersect(d_1, r, 1) → W
  41. Intersect(d_1, l) → Z,
  42. Intersect(d_1, k, 1) → A_1
  43. CircleSector(G, R, S) → e_1
  44. CircleSector(G, S, T) → f_1
  45. CircleSector(G, T, U) → g_1
  46. CircleSector(G, U, R) → h_1
  47. CircleSector(A, V, W) → k_1
  48. CircleSector(A, W, Z) → p_1
  49. CircleSector(A, Z, A_1) → q_1
  50. CircleSector(A, A_1, V) → r_1