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勾股定理无字证明 by Guillermo Bautista

勾股定理无字证明 by Guillermo Bautista
几何画板及绘图内容加载中，请稍等……
2016-12-12 10:56
测试改名0圆解析几何几何作图
所属专题 Use Cases of GeoGebra
①本范例通过动态演示证明勾股定理，即直角三角形两直角边的平方和等于斜边的平方；②涉及核心数学概念：勾股定理、解析几何、几何变换；③作图要点：使用Line、OrthogonalLine、Intersect、Circle、Distance、Polygon、Segment等GeoGebra命令构建图形；④适合高中数学教学或数学爱好者探索几何证明的直观性。

GeoGebra 命令及参数

  1. Line(A, B_1) → a
  2. Line(A, C) → b
  3. OrthogonalLine(C, b) → c_5
  4. Intersect(c_5, a) → B
  5. Circle(C, B) → d
  6. Intersect(d, b, 2) → D
  7. OrthogonalLine(B, c_5) → e
  8. OrthogonalLine(D, b) → f
  9. Intersect(e, f) → E
  10. Circle(C, A) → g
  11. OrthogonalLine(A, b) → h
  12. Intersect(g, c_5, 2) → F
  13. OrthogonalLine(F, c_5) → i
  14. Intersect(i, h) → G
  15. OrthogonalLine(A, a) → j
  16. OrthogonalLine(B, a) → k
  17. Circle(A, B) → p_1
  18. Intersect(p_1, j, 1) → H
  19. OrthogonalLine(H, j) → l
  20. Intersect(k, l) → I
  21. Intersect(f, i) → J
  22. Circle(D, ((p * Distance[J, D])) / Distance[F, J]) → r_2
  23. Distance(A, C) → s_1
  24. Distance(B, C) → s_2
  25. Distance(A, B) → s_3
  26. Circle(D, ((p * s_1)) / s_2) → s
  27. Circle(F, p) → q_1
  28. Circle(D, (p * s_1 / s_2)) → t
  29. Intersect(q_1, i, 1) → K
  30. Intersect(t, f, 2) → L
  31. Circle(L, s_2) → c_1
  32. Intersect(c_1, f, 1) → M
  33. Circle(K, s_1) → d_1
  34. Intersect(d_1, i, 2) → N
  35. Polygon(N, A, C, K) → poly1, n, a_1, c_2, k_1
  36. Polygon(L, C, B, M) → poly2, l_1, c_3, b_1, m
  37. Polygon(D, C, B, E) → poly3, d_2, c_4, b_2, e_1
  38. Segment(A, O) → f_1
  39. Segment(O, B) → g_1
  40. Line(P, g_1) → h_1
  41. Line(P, f_1) → i_1
  42. Intersect(f, h_1) → Q
  43. Intersect(i_1, i) → R
  44. Polygon(P, O, A, R) → poly4, p_2, o, a_2, r_1
  45. Polygon(P, Q, B, O) → poly5, p_3, q_2, b_3, o_1
  46. Polygon(V, S, U, Z) → poly6, v, s_4, u, z
  47. Polygon(W, T, S, V) → poly7, w, t_1, s_5, v_1
  48. Segment(D, C) → j_1
  49. Segment(D, E) → m_1
  50. Segment(E, B) → n_1
  51. Segment(C, B) → e_2
  52. Segment(C, A) → f_2
  53. Segment(G, A) → g_2
  54. Segment(F, C) → h_2
  55. Segment(F, G) → i_2
  56. Segment(J, F) → j_2
  57. Segment(J, D) → k_2
  58. Segment(A, H) → l_2
  59. Segment(A, B) → c
  60. Segment(B, I) → n_2
  61. Segment(H, I) → t_2
  62. Polygon(F, G, A, C) → poly8, f_3, g_3, a_3, c_6