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Geometric Proof of Pythagorean Theorem

Geometric Proof of Pythagorean Theorem
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2019-11-03 23:36
TriangleCircleVectorGeometric Construction
This example demonstrates the Pythagorean Theorem through geometric manipulation by dragging points. It involves core concepts like the Pythagorean Theorem, right triangles, and Cartesian coordinates. Construction highlights the use of GeoGebra commands such as Intersect, Point, Ray, Mirror, Semicircle, CircleArc, Segment, Polygon, Midpoint, OrthogonalLine, Vector, Centroid, and Translate. Ideal for middle school and above to explore and understand proofs of the Pythagorean Theorem.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Ray(A, B) → a
  4. Point(a) → C
  5. Mirror(C, A) → C'
  6. Semicircle(C, C') → c
  7. Intersect(c, yAxis) → D,
  8. CircleArc(A, D, C) → d
  9. Point(d) → E
  10. Segment(C, E) → b
  11. Segment(E, C') → e
  12. Segment(C', C) → f
  13. Polygon(C', C, 4) → poly1, g, h, i, j, F, G
  14. Polygon(C, E, 4) → poly2, k, l, m, n, H, I
  15. Polygon(E, C', 4) → poly3, p, q, r, s, J, K
  16. Midpoint(E, J) → L
  17. OrthogonalLine(L, i) → t
  18. OrthogonalLine(L, t) → a_1
  19. Intersect(a_1, s) → M
  20. Intersect(t, r) → N
  21. Intersect(a_1, q) → O
  22. Intersect(t, e) → P
  23. Polygon(M, L, N, K) → poly4, m_1, l_1, n_1, k_1
  24. Polygon(L, N, J, O) → poly5, l_2, n_2, j_1, o
  25. Polygon(L, P, C', O) → poly6, l_3, p_1, c', o_1
  26. Polygon(P, L, M, E) → poly7, p_2, l_4, m_2, e_1
  27. Vector(L, C) → u
  28. Vector(L, F) → v
  29. Vector(L, C') → w
  30. Vector(L, G) → u_1
  31. Centroid(poly4) → Q
  32. Centroid(poly5) → R
  33. Centroid(poly6) → S
  34. Centroid(poly7) → T
  35. Translate(T, w) → T'
  36. Translate(S, u) → S'
  37. Translate(R, v) → R'
  38. Translate(Q, u_1) → Q'
  39. Segment(Q, Q') → b_1
  40. Segment(R, R') → c_1
  41. Segment(S, S') → d_1
  42. Segment(T, T') → f_1
  43. Point(b_1) → U
  44. Point(c_1) → V
  45. Point(d_1) → W
  46. Point(f_1) → Z
  47. Vector(Q, U) → v_1
  48. Vector(R, V) → w_1
  49. Vector(S, W) → g_1
  50. Vector(T, Z) → h_1
  51. Translate(L, w_1) → L'
  52. Translate(N, w_1) → N'
  53. Translate(J, w_1) → J'
  54. Translate(O, w_1) → O'
  55. Polygon(L', N', J', O') → poly5', l', n', j', o'
  56. Translate(M, v_1) → M'
  57. Translate(L, v_1) → L'_1
  58. Translate(N, v_1) → N'_1
  59. Translate(K, v_1) → K'
  60. Polygon(M', L'_1, N'_1, K') → poly4', m', l'_1, n'_1, k'
  61. Translate(L, g_1) → L'_2
  62. Translate(P, g_1) → P'
  63. Translate(C', g_1) → C''
  64. Translate(O, g_1) → O'_1
  65. Polygon(L'_2, P', C'', O'_1) → poly6', l'_2, p', c'', o'_1
  66. Translate(P, h_1) → P'_1
  67. Translate(L, h_1) → L'_3
  68. Translate(M, h_1) → M'_1
  69. Translate(E, h_1) → E'
  70. Polygon(P'_1, L'_3, M'_1, E') → poly7', p'_1, l'_3, m'_1, e'
  71. Midpoint(H, C) → A_1
  72. Midpoint(C, G) → B_1
  73. Segment(A_1, B_1) → i_1
  74. Point(i_1) → C_1
  75. Vector(A_1, C_1) → q_1
  76. Translate(poly2, q_1) → poly2'