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毕达哥拉斯定理演示 by Kim Kelly

毕达哥拉斯定理演示 by Kim Kelly
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2012-03-03 21:59
测试改名0解析几何几何作图
该范例演示了毕达哥拉斯定理，即直角三角形的斜边平方等于两腰平方和。核心概念包括直角三角形、勾股定理和几何作图。通过使用GeoGebra命令如Segment、OrthogonalLine、Point等，可以动态展示三角形的构造过程。适合初中及以上学生学习几何和代数知识。

GeoGebra 命令及参数

  1. Segment(triPT_A, triPT_B) → a
  2. OrthogonalLine(triPT_B, a) → b
  3. Point(b) → triPT_C
  4. Ray(triPT_A, triPT_C) → c
  5. Angle(triPT_C, triPT_B, triPT_A) → α
  6. Polygon(triPT_A, triPT_C, triPT_B) → poly1, b_1, a_1, c_1
  7. OrthogonalLine(triPT_A, b_1) → d
  8. OrthogonalLine(triPT_C, b_1) → e
  9. OrthogonalLine(triPT_C, a_1) → f
  10. OrthogonalLine(triPT_B, a_1) → g
  11. OrthogonalLine(triPT_B, c_1) → h
  12. OrthogonalLine(triPT_A, c_1) → i
  13. Circle(triPT_A, triPT_C) → k
  14. Circle(triPT_C, triPT_B) → p
  15. Circle(triPT_B, triPT_A) → q
  16. Intersect(p, h) → F, G
  17. Intersect(q, h) → H, I
  18. Intersect(p, f) → L, M
  19. Intersect(k, d) → D, E
  20. OrthogonalLine(E, d) → j
  21. OrthogonalLine(I, h) → l
  22. OrthogonalLine(M, f) → m
  23. Intersect(j, e) → J
  24. Intersect(g, m) → K
  25. Intersect(l, i) → N
  26. Intersect(e, j) → O
  27. Polygon(triPT_A, triPT_C, O, E) → hypotSQUARE, a_2, c_2, o, e_1
  28. Polygon(triPT_A, N, I, triPT_B) → small_1SQUARE, a_3, n, i_1, b_2
  29. Polygon(triPT_B, K, M, triPT_C) → small_2SQUARE, b_3, k_1, m_1, c_3
  30. Angle(triPT_C, triPT_A, E) → β
  31. Angle(triPT_B, triPT_C, M) → γ
  32. Angle(triPT_A, triPT_B, I) → δ
  33. Line(triPT_B, b_1) → d_1
  34. Line(triPT_A, c_2) → f_1
  35. Intersect(d_1, a_3) → A
  36. Intersect(d_1, f_1) → B
  37. Intersect(f_1, n) → C
  38. Intersect(n, a_3) → P
  39. Polygon(C, B, A, P) → cut_1, c_4, b_4, a_4, p_1
  40. Intersect(i_1, n) → Q
  41. Polygon(C, B, triPT_B, Q) → cut_2, c_5, b_5, tript_b, q_1
  42. Polygon(A, triPT_A, B) → cut_3, b_6, a_5, tript_a
  43. Polygon(triPT_A, triPT_B, B) → cut_4, b_7, tript_1, tript_2
  44. Vector(B, triPT_A) → u
  45. Translate(triPT_A, u) → R
  46. Translate(triPT_B, u) → S
  47. Translate(B, u) → B'
  48. Polygon(R, S, B') → Tcut_4, b', r_2, s_1
  49. Intersect(e_1, o) → T
  50. Vector(B, T) → v
  51. Translate(C, v) → C'
  52. Translate(B, v) → B'_1
  53. Translate(triPT_B, v) → U
  54. Translate(Q, v) → Q'
  55. Polygon(C', B'_1, U, Q') → Tcut_2, c', b'_1, u_1, q'
  56. Intersect(o, c_2) → V
  57. Vector(B, V) → w
  58. Translate(C, w) → C'_1
  59. Translate(B, w) → B'_2
  60. Translate(A, w) → A'
  61. Translate(P, w) → P'
  62. Polygon(C'_1, B'_2, A', P') → Tcut_1, c'_1, b'_2, a', p'
  63. Vector(B, triPT_C) → z
  64. Translate(A, z) → A'_1
  65. Translate(triPT_A, z) → W
  66. Translate(B, z) → B'_3
  67. Polygon(A'_1, W, B'_3) → Tcut_3, b'_3, a'_1, w_1
  68. Intersect(k_1, b_3) → Z
  69. Intersect(m_1, k_1) → A_1
  70. Vector(Z, S) → v_1
  71. Translate(triPT_B, v_1) → B_1
  72. Translate(triPT_C, v_1) → C_1
  73. Translate(A_1, v_1) → D_1
  74. Translate(Z, v_1) → Z'
  75. Polygon(B_1, C_1, D_1, Z') → Tcopy, b_8, c_6, d_2, z'