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Pythagorean Theorem Demo

Pythagorean Theorem Demo
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2020-01-06 13:37
TriangleGeometric ConstructionSlider Animation
This example demonstrates the Pythagorean theorem in right triangles, showing the relationship between the lengths of the sides. Key math concepts include the Pythagorean theorem, right triangles, and side length calculations. It is constructed using commands like Polygon, Segment, Intersect, Mirror, Point, Textfield, Vector, Translate, and Dilate. Suitable for middle school students and above to learn and understand the theorem.

GeoGebra Commands & Parameters

  1. Polygon(B, A, 4) → poly1, c, d, e, f, C, D
  2. Segment(E, F) → h
  3. Segment(G, H) → i
  4. Intersect(h, i) → I
  5. Polygon(C, E, I, H) → poly2, c_1, e_1, i_1, h_1
  6. Polygon(H, I, F, A) → poly3, h_2, i_2, f_1, a_1
  7. Polygon(I, G, B, F) → poly4, i_3, g_1, b_1, f_2
  8. Polygon(E, D, G, I) → poly5, e_2, d_1, g_2, i_4
  9. Mirror(C, l) → C'
  10. Mirror(E, l) → E'
  11. Mirror(I, l) → I'
  12. Mirror(H, l) → H'
  13. Polygon(C', E', I', H') → poly2', c', e', i', h'
  14. Mirror(H, j) → H'_1
  15. Mirror(I, j) → I'_1
  16. Mirror(F, j) → F'
  17. Mirror(A, j) → A'
  18. Polygon(H'_1, I'_1, F', A') → poly3', h'_1, i'_1, f', a'
  19. Mirror(I, m) → I'_2
  20. Mirror(G, m) → G'
  21. Mirror(B, m) → B'
  22. Mirror(F, m) → F'_1
  23. Polygon(I'_2, G', B', F'_1) → poly4', i'_2, g', b', f'_1
  24. Mirror(E, k) → E'_1
  25. Mirror(D, k) → D'
  26. Mirror(G, k) → G'_1
  27. Mirror(I, k) → I'_3
  28. Polygon(E'_1, D', G'_1, I'_3) → poly5', e'_1, d', g'_1, i'_3
  29. Point(Circle[O, r]) → P
  30. Segment(O, P) → s
  31. Polygon(O, P, 4) → poly6, t, j_1, p_1, q_1, Q, R
  32. Textfield(a) → inputBox1
  33. Textfield(r) → inputBox2
  34. Textfield(b) → inputBox3
  35. Intersect(f, d') → U
  36. Intersect(f, d') → V
  37. Vector(E', E'_1) → u
  38. Translate(C', u) → C''
  39. Translate(E', u) → E''
  40. Translate(I', u) → I''
  41. Translate(H', u) → H''
  42. Polygon(C'', E'', I'', H'') → poly2'', c'', e'', i'', h''
  43. Vector(H'_1, H'') → v
  44. Translate(H'_1, v) → J
  45. Translate(I'_1, v) → K
  46. Translate(F', v) → F''
  47. Translate(A', v) → A''
  48. Polygon(J, K, F'', A'') → poly3'', j_2, k_1, f'', a''
  49. Vector(G', G'_1) → w
  50. Translate(I'_2, w) → L
  51. Translate(G', w) → G''
  52. Translate(B', w) → B''
  53. Translate(F'_1, w) → M
  54. Dilate(E'_1, n, E') → N
  55. Vector(E', N) → p
  56. Translate(C', p) → C''_1
  57. Translate(E', p) → E''_1
  58. Translate(I', p) → I''_1
  59. Translate(H', p) → H''_1
  60. Polygon(C''_1, E''_1, I''_1, H''_1) → poly2''_1, c''_1, e''_1, i''_1, h''_1
  61. Dilate(H'', n - 1, H'_1) → H'''
  62. Vector(H'_1, H''') → u_1
  63. Translate(H'_1, u_1) → W
  64. Translate(I'_1, u_1) → Z
  65. Translate(F', u_1) → F''_1
  66. Translate(A', u_1) → A''_1
  67. Polygon(W, Z, F''_1, A''_1) → poly3''_1, w_1, z_1, f''_1, a''_1
  68. Dilate(G'_1, n - 2, G') → C_1
  69. Vector(G', C_1) → v_1
  70. Translate(I'_2, v_1) → D_1
  71. Translate(G', v_1) → G''_1
  72. Translate(B', v_1) → B''_1
  73. Translate(F'_1, v_1) → E_1
  74. Polygon(D_1, G''_1, B''_1, E_1) → poly4''_1, d_2, g''_1, b''_1, e_3
  75. Dilate(B'', t_1, O) → B'''
  76. Vector(O, B''') → n_1
  77. Translate(poly6, n_1) → poly6'
  78. Segment(B', G') → l_1
  79. Segment(E''_1, C''_1) → m_1
  80. Segment(C''_1, H''_1) → a_2
  81. Segment(E'', C'') → b_2
  82. Segment(H'', C'') → c_2

AI Drawing Prompt Reference

Draw a right triangle with labeled side lengths, fill the areas of the squares on the two legs and the hypotenuse to demonstrate the Pythagorean theorem. Include a slider to adjust the triangle's size, and use reflection and vector tools to create auxiliary shapes for verification.
The prompt above was compiled from the original drawing commands and is for reference only.