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三平行线定理探索

三平行线定理探索
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2019-05-23 02:46
测试改名0解析几何几何作图
本范例通过几何作图探索三平行线定理。核心概念包括平行线、距离和三角形。使用GeoGebra命令如Line、Distance、Point等进行构造。适合初中及以上学生学习几何证明和探索性质。

GeoGebra 命令及参数

  1. Line(A, B) → a_1
  2. Circle(A, a) → c
  3. OrthogonalLine(A, a_1) → b
  4. Intersect(c, b, 1) → C
  5. OrthogonalLine(C, b) → d
  6. Intersect(c, b) → D, E
  7. OrthogonalLine(E, b) → e
  8. Circle(E, a) → f
  9. Intersect(f, b, 2) → F
  10. OrthogonalLine(F, b) → g
  11. Circle(C, a) → h
  12. Intersect(h, b) → G, H
  13. OrthogonalLine(G, b) → i
  14. Distance(F, E) → distanceFE
  15. Distance(E, A) → distanceEA
  16. Distance(A, C) → distanceAC
  17. Distance(C, G) → distanceCG
  18. Point(b) → I
  19. Point(b) → J
  20. Point(g) → K
  21. Point(i) → L
  22. Line(K, L) → j
  23. Intersect(e, j) → O
  24. Intersect(a_1, j) → P
  25. Intersect(d, j) → Q
  26. Segment(K, O) → k
  27. Segment(O, P) → l
  28. Segment(P, Q) → m
  29. Segment(Q, L) → n
  30. Point(g) → M
  31. Point(i) → N
  32. Segment(M, N) → p
  33. Intersect(e, p) → R
  34. Intersect(a_1, p) → S
  35. Intersect(d, p) → T
  36. Segment(M, R) → q
  37. Segment(R, S) → r
  38. Segment(S, T) → s
  39. Segment(T, N) → t
  40. Circle(N, 3) → c_1
  41. Circle(T, 3) → d_1
  42. Circle(S, 3) → e_1
  43. Circle(R, 3) → f_1
  44. Intersect(f_1, e, 1) → U
  45. Intersect(f_1, q, 1) → V
  46. Intersect(e_1, a_1, 2) → W
  47. Intersect(e_1, r, 1) → Z
  48. Intersect(d_1, d, 1) → A_1
  49. Intersect(d_1, s, 1) → B_1
  50. Intersect(c_1, i, 1) → C_1
  51. Intersect(c_1, t, 1) → D_1
  52. CircleSector(R, U, V) → g_1
  53. CircleSector(S, W, Z) → h_1
  54. CircleSector(T, A_1, B_1) → k_1
  55. CircleSector(N, C_1, D_1) → p_1