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Pythagorean Theorem Demonstration by PopiArdv

Pythagorean Theorem Demonstration by PopiArdv
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2013-01-16 03:11
TriangleCircleFunctionCoordinate GeometryGeometric Construction
This example visually demonstrates the Pythagorean theorem in right-angled triangles, illustrating the relationship between the lengths of the three sides. Key math concepts include the Pythagorean theorem, right triangles, and analytical geometry. It utilizes GeoGebra commands and objects such as Polygon, OrthogonalLine, Semicircle, Point, Ray, Intersect, Segment, Circle, Line, and Angle. Suitable for middle school students and above to learn and understand the theorem and its applications.

GeoGebra Commands & Parameters

  1. Polygon(Β, Α, 4) → πολύγ4, k, l, m, n, Θ, Ι
  2. OrthogonalLine(Β, k) → s
  3. Semicircle(Α, Β) → c
  4. Point(c) → Γ
  5. Polygon(Γ, Β, 4) → πολύγ3, g, h, i, j, Ζ, Η
  6. Ray(Ζ, Η) → q
  7. Polygon(Α, Γ, 4) → πολύγ2, b, d, e, f, Δ, Ε
  8. Ray(Ε, Δ) → p
  9. Intersect(p, q) → Μ
  10. Segment(Μ, Ζ) → e_1
  11. Segment(Α, Β) → a
  12. Polygon(Γ, Α, Β) → πολύγ1, β_1, γ, α_1
  13. OrthogonalLine(Α, k) → r
  14. Intersect(r, p) → Κ
  15. Segment(Α, Κ) → t
  16. Intersect(s, e_1) → Λ
  17. Segment(Λ, Β) → a_1
  18. OrthogonalLine(Μ, k) → b_1
  19. Intersect(b_1, k) → Ν
  20. Segment(Μ, Ν) → c_1
  21. Segment(Μ, Ε) → d_1
  22. Segment(Ν, Α) → f_1
  23. Segment(Ν, Β) → g_1
  24. Circle(Γ, v) → h_1
  25. Intersect(h_1, c_1) → Ξ, Ο
  26. Circle(Δ, δ) → k_1
  27. Intersect(k_1, d_1) → Π, Ρ
  28. Circle(Ν, w) → p_1
  29. Line(Γ, Μ) → i_1
  30. Intersect(p_1, i_1, 1) → Σ
  31. Circle(Π, b) → q_1
  32. Intersect(e, d_1) → Υ
  33. Intersect(q_1, d_1) → Φ, Χ
  34. Polygon(Χ, Α, Γ, Π) → πολύγ5, χ, α_2, γ_1, π
  35. Circle(Ο, k) → r_1
  36. Intersect(i_1, c_1) → Ψ
  37. Intersect(r_1, i_1) → Ω, Α_1
  38. Polygon(Κ, Α_1, Ο, Α) → πολύγ6, κ, α_3, ο, α_4
  39. OrthogonalLine(Σ, l) → j_1
  40. Intersect(j_1, l) → Β_1
  41. Circle(Σ, k) → s_1
  42. Intersect(i_1, c_1) → Γ_1
  43. Intersect(i_1, c_1) → Δ_1
  44. Intersect(i_1, c_1) → Ε_1
  45. Intersect(i_1, c_1) → Ζ_1
  46. Intersect(i_1, c_1) → Η_1
  47. Intersect(i_1, c_1) → Θ_1
  48. Intersect(i_1, c_1) → Ι_1
  49. Intersect(s_1, i_1) → Κ_1, Λ_1
  50. OrthogonalLine(Λ_1, t) → l_1
  51. Intersect(t, α_4) → Ο_1
  52. Intersect(l_1, t) → Π_1
  53. Polygon(Π_1, Λ_1, Σ, Β_1) → πολύγ7, π_1, λ_1, σ, β_2
  54. Intersect(i_1, λ_1) → Μ_1
  55. Intersect(m, i_1) → Ν_1
  56. Polygon(Α, Ν, Ν_1, Θ) → πολύγ8, α_5, ν, ν_1, θ
  57. Circle(Γ, ζ) → d_2
  58. Intersect(d_2, c_1) → Υ_1, Φ_1
  59. Circle(Φ_1, k) → f_2
  60. Intersect(f_2, c_1, 1) → Χ_1
  61. Polygon(Λ, Χ_1, Φ_1, Β) → πολύγ10, λ, χ_1, φ_1, β_4
  62. Ray(Μ, Ζ) → m_1
  63. Circle(Ν, z) → g_2
  64. Ray(Γ, Ν) → n_1
  65. Intersect(m, n_1) → Σ_1
  66. Intersect(g_2, n_1) → Ψ_1, Ω_1
  67. OrthogonalLine(Ω_1, n_1) → a_2
  68. Circle(Ω_1, k) → h_2
  69. Intersect(h_2, c_1) → Β_2,
  70. OrthogonalLine(Β_2, t) → b_2
  71. Intersect(b_2, a_1) → Γ_2
  72. Intersect(n, a_2) → Δ_2
  73. Polygon(Β_2, Γ_2, Δ_2, Ω_1) → πολύγ11, β_5, γ_3, δ_2, ω_1
  74. Circle(Η, ε) → t_1
  75. Ray(Η, Μ) → c_2
  76. Intersect(t_1, e_1) → Τ_1, Τ
  77. Angle(Α, Γ, Β) → β
  78. Polygon(Ν, Β, Ι, Ν_1) → πολύγ12, ν_2, β_6, ι, ν_3
  79. Circle(Τ_1, g) → k_2
  80. Intersect(k_2, m_1) → Ρ_1, Α_2
  81. Point(β_6) → Ε_2
  82. Polygon(Τ_1, Α_2, Β, Γ) → πολύγ9, τ_1, α_6, β_3, γ_2

AI Drawing Prompt Reference

Draw a right triangle to demonstrate the Pythagorean theorem, using a semicircle and squares to illustrate the relationship between the lengths of the three sides. Start by drawing the right triangle, then draw a semicircle with the hypotenuse as the diameter. Construct squares on each side of the triangle and compare their areas. Add auxiliary lines, circles, and intersection points to clearly show the geometric proof of the theorem.
The prompt above was compiled from the original drawing commands and is for reference only.