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动态勾股定理图形演示

动态勾股定理图形演示
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2016-03-31 14:16
测试改名0角几何作图
该范例通过动态图形演示勾股定理。它展示了直角三角形的两个直角边的平方和等于斜边的平方。核心数学概念包括直角三角形、勾股定理和角度。使用了Segment、OrthogonalLine、Point、Rotate、Intersect、Angle、Midpoint、Text、Polygon等GeoGebra命令。适合初中及以上学生学习几何和证明。

GeoGebra 命令及参数

  1. Segment(A, B) → a
  2. OrthogonalLine(A, a) → b
  3. Point(b) → C
  4. Segment(A, C) → c
  5. Segment(C, B) → d
  6. Rotate(C, 90°, C) → C'
  7. Rotate(B, 90°, C) → B'
  8. Segment(C', B') → d'
  9. Rotate(C', 90°, B') → C''
  10. Rotate(B', 90°, B') → B''
  11. Segment(C'', B'') → d''
  12. Segment(C'', B) → e
  13. OrthogonalLine(B', b) → g
  14. Intersect(b, g) → D
  15. Segment(C, D) → f
  16. Segment(D, B') → h
  17. OrthogonalLine(C'', g) → i
  18. Intersect(g, i) → E
  19. Segment(B', E) → j
  20. Segment(E, C'') → k
  21. OrthogonalLine(B, i) → l
  22. Segment(E, C'') → m
  23. Intersect(i, l) → F
  24. Segment(C'', F) → n
  25. Segment(F, B) → p
  26. Angle(C, D, B') → α
  27. Angle(B', E, C'') → β
  28. Angle(B, F, C'') → γ
  29. Angle(d', d) → δ
  30. Angle(C, A, B) → ε
  31. Angle(C, B, C'') → ζ
  32. Angle(B'', C'', B) → η
  33. Angle(d'', d) → θ
  34. Intersect(d', d'') → H
  35. Angle(C, B, A) → κ
  36. Angle(B, C'', F) → λ
  37. Angle(f, d') → μ
  38. Angle(A, C, B) → ν
  39. Angle(D, B', C') → ξ
  40. Angle(B'', C'', E) → ο
  41. Angle(C'', B, F) → ρ
  42. Intersect(d', d'') → K
  43. Midpoint(k) → M
  44. Midpoint(n) → N
  45. Midpoint(p) → O
  46. Midpoint(a) → P
  47. Text(" a", M) → text9
  48. Text(" b", N) → text10
  49. Midpoint(c) → S
  50. Midpoint(f) → LL
  51. Midpoint(h) → U
  52. Midpoint(j) → V
  53. Midpoint(d'') → G
  54. Angle(G, H, V) → ι
  55. Point(Circle[V, 0.3844228700967704]) → I
  56. Polygon(V, I, J) → poly1, j_1, v, i_1
  57. Point(Circle[U, 0.29763004734908566]) → L
  58. Polygon(U, L, R) → poly2, r, u, l_1
  59. Point(Circle[LL, 0.333181955679241]) → T
  60. Polygon(LL, T, Z) → poly3, z_1, w, t
  61. Point(Circle[S, 0.44269092479036803]) → Q
  62. Text(text2, P) → text3
  63. Text(text1, O) → text4
  64. Text("a", L) → text7
  65. Text("a", Q) → text8
  66. Text("b", I) → text11
  67. Text("b", T) → text12
  68. Angle(C, H, G) → σ