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Pythagoras Theorem Demonstration by Kim Kelly

Pythagoras Theorem Demonstration by Kim Kelly
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2012-03-03 21:59
TriangleCoordinate GeometryGeometric Construction
This example demonstrates the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Key concepts include right triangles, Pythagorean theorem, and geometric construction. Using GeoGebra commands such as Segment, OrthogonalLine, Point, etc., the construction process of the triangle can be dynamically shown. Suitable for students at the junior high school level and above to learn geometry and algebra.

GeoGebra Commands & Parameters

  1. Segment(triPT_A, triPT_B) → a
  2. OrthogonalLine(triPT_B, a) → b
  3. Point(b) → triPT_C
  4. Ray(triPT_A, triPT_C) → c
  5. Angle(triPT_C, triPT_B, triPT_A) → α
  6. Polygon(triPT_A, triPT_C, triPT_B) → poly1, b_1, a_1, c_1
  7. OrthogonalLine(triPT_A, b_1) → d
  8. OrthogonalLine(triPT_C, b_1) → e
  9. OrthogonalLine(triPT_C, a_1) → f
  10. OrthogonalLine(triPT_B, a_1) → g
  11. OrthogonalLine(triPT_B, c_1) → h
  12. OrthogonalLine(triPT_A, c_1) → i
  13. Circle(triPT_A, triPT_C) → k
  14. Circle(triPT_C, triPT_B) → p
  15. Circle(triPT_B, triPT_A) → q
  16. Intersect(p, h) → F, G
  17. Intersect(q, h) → H, I
  18. Intersect(p, f) → L, M
  19. Intersect(k, d) → D, E
  20. OrthogonalLine(E, d) → j
  21. OrthogonalLine(I, h) → l
  22. OrthogonalLine(M, f) → m
  23. Intersect(j, e) → J
  24. Intersect(g, m) → K
  25. Intersect(l, i) → N
  26. Intersect(e, j) → O
  27. Polygon(triPT_A, triPT_C, O, E) → hypotSQUARE, a_2, c_2, o, e_1
  28. Polygon(triPT_A, N, I, triPT_B) → small_1SQUARE, a_3, n, i_1, b_2
  29. Polygon(triPT_B, K, M, triPT_C) → small_2SQUARE, b_3, k_1, m_1, c_3
  30. Angle(triPT_C, triPT_A, E) → β
  31. Angle(triPT_B, triPT_C, M) → γ
  32. Angle(triPT_A, triPT_B, I) → δ
  33. Line(triPT_B, b_1) → d_1
  34. Line(triPT_A, c_2) → f_1
  35. Intersect(d_1, a_3) → A
  36. Intersect(d_1, f_1) → B
  37. Intersect(f_1, n) → C
  38. Intersect(n, a_3) → P
  39. Polygon(C, B, A, P) → cut_1, c_4, b_4, a_4, p_1
  40. Intersect(i_1, n) → Q
  41. Polygon(C, B, triPT_B, Q) → cut_2, c_5, b_5, tript_b, q_1
  42. Polygon(A, triPT_A, B) → cut_3, b_6, a_5, tript_a
  43. Polygon(triPT_A, triPT_B, B) → cut_4, b_7, tript_1, tript_2
  44. Vector(B, triPT_A) → u
  45. Translate(triPT_A, u) → R
  46. Translate(triPT_B, u) → S
  47. Translate(B, u) → B'
  48. Polygon(R, S, B') → Tcut_4, b', r_2, s_1
  49. Intersect(e_1, o) → T
  50. Vector(B, T) → v
  51. Translate(C, v) → C'
  52. Translate(B, v) → B'_1
  53. Translate(triPT_B, v) → U
  54. Translate(Q, v) → Q'
  55. Polygon(C', B'_1, U, Q') → Tcut_2, c', b'_1, u_1, q'
  56. Intersect(o, c_2) → V
  57. Vector(B, V) → w
  58. Translate(C, w) → C'_1
  59. Translate(B, w) → B'_2
  60. Translate(A, w) → A'
  61. Translate(P, w) → P'
  62. Polygon(C'_1, B'_2, A', P') → Tcut_1, c'_1, b'_2, a', p'
  63. Vector(B, triPT_C) → z
  64. Translate(A, z) → A'_1
  65. Translate(triPT_A, z) → W
  66. Translate(B, z) → B'_3
  67. Polygon(A'_1, W, B'_3) → Tcut_3, b'_3, a'_1, w_1
  68. Intersect(k_1, b_3) → Z
  69. Intersect(m_1, k_1) → A_1
  70. Vector(Z, S) → v_1
  71. Translate(triPT_B, v_1) → B_1
  72. Translate(triPT_C, v_1) → C_1
  73. Translate(A_1, v_1) → D_1
  74. Translate(Z, v_1) → Z'
  75. Polygon(B_1, C_1, D_1, Z') → Tcopy, b_8, c_6, d_2, z'