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Proof Without Words by Steve Phelps (8)

Proof Without Words by Steve Phelps (8)
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2015-12-13 09:03
TriangleCircleGeometric Construction
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This example dynamically demonstrates the Pythagorean Theorem, illustrating the relationship between the sides of a right triangle. It involves core math concepts like the Pythagorean Theorem, right triangles, linear equations, and circles. Construction uses commands such as Point, Mirror, Semicircle, Circle, Polygon, OrthogonalLine, Intersect, Vector, and Translate in GeoGebra. Ideal for high school mathematics teaching or exploration by math enthusiasts.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(yAxis) → B
  3. Mirror(A, B) → A'
  4. Semicircle(A, A') → s
  5. Circle(B, A') → c
  6. Point(s) → C
  7. Polygon(A, C, 4) → poly1, a, b, d, e, D, E
  8. Polygon(C, A', 4) → poly2, f, g, h, i, F, G
  9. Polygon(A', A, 4) → poly3, j, k, l, m, H, I
  10. OrthogonalLine(A', j) → n
  11. OrthogonalLine(C, n) → p
  12. Intersect(n, p) → J
  13. Intersect(n, h) → K
  14. Intersect(p, h) → L
  15. Intersect(n, i) → M
  16. Intersect(p, g) → N
  17. Polygon(C, J, A') → poly4, a', c_1, j_1
  18. Polygon(A', J, N) → poly5, n_1, a'_1, j_2
  19. Polygon(J, K, F, N) → poly6, j_3, k_1, f_1, n_2
  20. Polygon(J, K, G, C) → poly7, j_4, k_2, g_1, c_2
  21. Polygon(C, J, M) → poly8, m_1, c_3, j_5
  22. Polygon(J, M, G, L) → poly9, j_6, m_2, g_2, l_1
  23. Polygon(J, A', F, L) → poly10, j_7, a'_2, f_2, l_2
  24. Vector(J, A') → u
  25. Translate(C, u) → C'
  26. Translate(J, u) → J'
  27. Translate(A', u) → A''
  28. Polygon(C', J', A'') → poly4', a'', c', j'
  29. Vector(J, I) → v
  30. Translate(J, v) → J'_1
  31. Translate(K, v) → K'
  32. Translate(G, v) → G'
  33. Translate(C, v) → C'_1
  34. Polygon(J'_1, K', G', C'_1) → poly7', j'_1, k', g', c'_1
  35. Translate(C, v) → C'_2
  36. Translate(J, v) → J'_2
  37. Translate(M, v) → M'
  38. Polygon(C'_2, J'_2, M') → poly8', m', c'_2, j'_2
  39. Vector(J, A) → w
  40. Translate(A', w) → A''_1
  41. Translate(J, w) → J'_3
  42. Translate(N, w) → N'
  43. Polygon(A''_1, J'_3, N') → poly5', n', a''_1, j'_3
  44. Translate(J, w) → J'_4
  45. Translate(A', w) → A''_2
  46. Translate(F, w) → F'
  47. Translate(L, w) → L'
  48. Polygon(J'_4, A''_2, F', L') → poly10', j'_4, a''_2, f', l'
  49. Vector(J, H) → q
  50. Translate(J, q) → J'_5
  51. Translate(M, q) → M'_1
  52. Translate(G, q) → G'_1
  53. Translate(L, q) → L'_1
  54. Polygon(J'_5, M'_1, G'_1, L'_1) → poly9', j'_5, m'_1, g'_1, l'_1
  55. Translate(J, q) → J'_6
  56. Translate(K, q) → K'_1
  57. Translate(F, q) → F'_1
  58. Translate(N, q) → N'_1
  59. Polygon(J'_6, K'_1, F'_1, N'_1) → poly6', j'_6, k'_1, f'_1, n'_1
  60. Polygon(A, E, D, C) → poly11, a_1, e_1, d_1, c_4
  61. Vector(D, C') → r
  62. Translate(A, r) → A'_1
  63. Translate(E, r) → E'
  64. Translate(D, r) → D'
  65. Translate(C, r) → C'_3
  66. Polygon(A'_1, E', D', C'_3) → poly11', a'_3, e', d', c'_3