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Pythagorean Theorem Proof Without Words by Guillermo Bautista

Pythagorean Theorem Proof Without Words by Guillermo Bautista
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2016-12-12 10:56
TriangleCircleCoordinate GeometryGeometric Construction
In collections Use Cases of GeoGebra
This example dynamically demonstrates the Pythagorean Theorem, showing that in a right triangle, the square of the two legs equals the square of the hypotenuse. It involves core concepts like the Pythagorean Theorem, coordinate geometry, and geometric transformations. Constructed using commands such as Line, OrthogonalLine, Intersect, Circle, Distance, Polygon, and Segment in GeoGebra. Suitable for high school mathematics teaching or exploration by math enthusiasts for intuitive geometric proofs.

GeoGebra Commands & Parameters

  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