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勾股定理演示 by Duane Habecker

勾股定理演示 by Duane Habecker
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2018-11-19 07:48
测试改名0几何作图
①本范例通过动态演示直角三角形三边关系，直观展示勾股定理的应用；②核心数学概念为勾股定理、直角三角形、距离计算；③构造要点：使用 Circle, Line, Intersect, Point, Segment, Rotate, OrthogonalLine, Polygon 等命令绘制并交互验证定理；④适合初中及以上学生及数学爱好者学习几何定理验证与证明。

GeoGebra 命令及参数

  1. Circle(A, B) → c_1
  2. Line(B, A) → c_2
  3. Intersect(c_1, c_2, 2) → C
  4. Point(c_1) → D
  5. Segment(C, D) → a
  6. Segment(D, B) → b
  7. Rotate(D, 90°, C) → E
  8. Rotate(C, 90°, E) → F
  9. Rotate(B, 90°, D) → G
  10. Rotate(D, 90°, G) → H
  11. Rotate(C, 90°, B) → I
  12. Rotate(B, 90°, I) → J
  13. Segment(C, B) → c
  14. OrthogonalLine(G, c) → d
  15. OrthogonalLine(B, c) → e
  16. Segment(G, H) → f
  17. Intersect(e, f) → K
  18. Segment(G, K) → g
  19. Point(g) → L
  20. Line(H, c) → h
  21. Line(D, c) → i
  22. Segment(D, G) → j
  23. Segment(B, H) → k
  24. Intersect(h, j) → M
  25. Segment(D, M) → l
  26. Point(l) → N
  27. Segment(G, H) → m
  28. OrthogonalLine(L, c) → n
  29. Line(N, c) → p
  30. Intersect(n, p) → O
  31. Intersect(b, n) → P
  32. Intersect(k, p) → Q
  33. Segment(L, H) → q
  34. Segment(L, O) → r
  35. Segment(O, Q) → s
  36. Segment(Q, H) → t
  37. Circle(R, (0.5 * s)) → c1
  38. Line(R, s) → a1
  39. Intersect(c1, a1, 1) → S
  40. Intersect(c1, a1, 2) → T
  41. Circle(S, r) → d1
  42. OrthogonalLine(S, a1) → b1
  43. Intersect(d1, b1, 2) → U
  44. Circle(U, q) → e1
  45. Circle(T, t) → f1
  46. Intersect(e1, f1, 1) → V
  47. Segment(N, O) → g1
  48. Segment(N, G) → h1
  49. Segment(G, L) → i1
  50. Circle(W, (0.5 * g1)) → k1
  51. Line(W, g1) → j1
  52. Intersect(k1, j1, 1) → Z
  53. Intersect(k1, j1, 2) → A1
  54. Circle(A1, r) → p1
  55. OrthogonalLine(A1, j1) → l1
  56. Intersect(p1, l1, 2) → B1
  57. Circle(Z, h1) → q1
  58. Circle(B1, i1) → r1
  59. Intersect(q1, r1, 1) → C1
  60. Segment(N, D) → m1
  61. Segment(D, P) → n1
  62. Segment(P, O) → s1
  63. Circle(D1, (0.25 * s1)) → t1
  64. Line(D1, s1) → a2
  65. Intersect(t1, a2, 2) → E1
  66. OrthogonalLine(E1, a2) → b2
  67. Circle(E1, s1) → c2
  68. Intersect(c2, a2, 1) → F1
  69. Circle(E1, g1) → d2
  70. Intersect(d2, b2, 2) → G1
  71. Circle(G1, m1) → e2
  72. Circle(F1, n1) → f2
  73. Intersect(e2, f2, 2) → H1
  74. Segment(P, B) → g2
  75. Segment(B, Q) → h2
  76. Circle(I1, (0.5 * s1)) → k2
  77. Line(I1, s1) → i2
  78. Intersect(k2, i2, 2) → J1
  79. Intersect(k2, i2, 1) → K1
  80. OrthogonalLine(J1, i2) → j2
  81. Circle(J1, s) → p2
  82. Intersect(p2, j2, 1) → L1
  83. Circle(L1, h2) → q2
  84. Circle(K1, g2) → r2
  85. Intersect(q2, r2, 1) → M1
  86. Polygon(Z, A1, B1, C1) → poly1, z, a1_1, b1_1, c1_1
  87. Polygon(J1, K1, M1, L1) → poly2, j1_1, k1_1, m1_1, l1_1
  88. Polygon(U, S, T, V) → poly3, u, s_1, t_1, v
  89. Polygon(G1, H1, F1, E1) → poly4, g1_1, h1_1, f1_1, e1_1
  90. Segment(E, F) → l2
  91. Circle(N1, a) → s2
  92. Line(N1, a) → m2
  93. Intersect(s2, m2, 2) → O1
  94. OrthogonalLine(O1, m2) → n2
  95. OrthogonalLine(N1, m2) → t2
  96. Intersect(s2, t2, 2) → P1
  97. Circle(O1, a) → c3
  98. Intersect(c3, n2, 2) → Q1
  99. Polygon(N1, O1, Q1, P1) → poly5, n1_1, o1, q1_1, p1_1
  100. Segment(E, C) → a3
  101. Segment(F, D) → b3
  102. Segment(C, J) → d3
  103. Segment(J, I) → e3
  104. Segment(I, B) → f3
  105. Polygon(D, C, B) → poly6, b_1, d_1, c_3