MathPlotAI Logo MathPlotAI

Rhombus Folding Demonstration

Rhombus Folding Demonstration
Loading the math board and drawing, please wait…
2018-02-26 17:51
PolygonTransformationGeometric Construction
In collections Folding paper, doing geometry figures
This example demonstrates the geometric transformation and symmetry of a rhombus through folding. It involves core mathematical concepts such as polygon properties, angle bisectors, symmetry axes, rotation, and reflection. The construction utilizes GeoGebra commands and objects like Polygon, Segment, Midpoint, Rotate, CircleArc, Intersect, AngularBisector, OrthogonalLine, Mirror, Circle, and Line. It is suitable for high school geometry teaching to understand rhombus symmetry and transformation geometry.

GeoGebra Commands & Parameters

  1. Polygon(A, C, D, B) → vierhoek1, a, c, d, b
  2. Segment((sqrt(2) / 4, 0), (sqrt(2) / 4, 1)) → f
  3. Segment((sqrt(2) / 2, 0), (sqrt(2) / 2, 1)) → g
  4. Segment(((3 * sqrt(2) / 4), 0), ((3 * sqrt(2) / 4), 1)) → h
  5. Midpoint(B, D) → E
  6. Rotate(D, -90°, E) → DD
  7. CircleArc(E, DD, D) → e
  8. Intersect(e, h, 1) → F
  9. CircleArc(E, F, D) → k
  10. AngularBisector(F, E, D) → i
  11. Intersect(i, c) → G
  12. Segment(E, G) → j
  13. Polygon(A, C, G, E, B) → veelhoek1, a_1, c_1, g_1, e_1, b_1
  14. Polygon(E, D, G) → driehoek1, g_2, e_2, d_1
  15. Rotate(E, (((-(s - 1)) * 180))°, g_1) → E'
  16. Rotate(D, (((-(s - 1)) * 180))°, g_1) → D'
  17. Rotate(G, (((-(s - 1)) * 180))°, g_1) → G'
  18. Polygon(E', D', G') → driehoek1', g', e', d'
  19. Polygon(E, F, G) → driehoek2, g_3, e_3, f_1
  20. Segment(E, D) → l
  21. Segment(D, G) → m
  22. OrthogonalLine(F, a_1) → n
  23. Intersect(j, d') → HH
  24. Intersect(j, d') → II
  25. Intersect(n, j) → R
  26. Intersect(n, a_1) → S
  27. Segment(R, S) → p
  28. Segment(F, S) → q
  29. Mirror(F, g) → H
  30. Mirror(G, g) → I
  31. Segment(I, E) → r
  32. CircleArc(E, B, H) → t
  33. Polygon(I, E, B) → driehoek3, b_2, i_1, e_4
  34. Rotate(I, (((s - 3) * 180))°, r) → I'
  35. Rotate(E, (((s - 3) * 180))°, r) → E'_1
  36. Rotate(B, (((s - 3) * 180))°, r) → B'
  37. Polygon(I', E'_1, B') → driehoek3', b', i', e'_1
  38. Polygon(E, I, A, C, G) → veelhoek2, e_5, i_2, a_2, c_2, g_4
  39. Segment(B, E) → h_1
  40. Segment(B, I) → j_1
  41. Mirror(R, g) → TT
  42. Mirror(S, g) → SS
  43. Segment(SS, TT) → k_1
  44. Segment(SS, H) → l_1
  45. Polygon(I, H, E) → driehoek4, e_6, i_3, h_2
  46. Circle(G, C) → p_1
  47. Intersect(d', f_1) → J
  48. Intersect(d', f_1) → K
  49. Intersect(d', f_1) → L
  50. Intersect(d', f_1) → M
  51. Intersect(p_1, f_1) → N,
  52. CircleArc(G, N, C) → q_1
  53. Line(G, F) → m_1
  54. Intersect(m_1, a_2) → O
  55. Segment(O, F) → n_1
  56. Polygon(O, C, G) → driehoek5, g_5, o, c_3
  57. Rotate(O, (((s - 5) * 180))°, c_3) → O'
  58. Rotate(C, (((s - 5) * 180))°, c_3) → C'
  59. Rotate(G, (((s - 5) * 180))°, c_3) → G'_1
  60. Polygon(O', C', G'_1) → driehoek5', g'_1, o', c'
  61. Polygon(I, A, O, G, E) → veelhoek3, i_4, a_3, o_1, g_6, e_7
  62. Mirror(O, n_1) → O'_1
  63. Mirror(C, n_1) → C'_1
  64. Mirror(G, n_1) → G'_2
  65. Polygon(O'_1, C'_1, G'_2) → driehoek5'_1, g'_2, o'_1, c'_1
  66. Mirror(O, g) → O'_2
  67. Mirror(C, g) → C'_2
  68. Mirror(G, g) → G'_3
  69. Polygon(O'_2, C'_2, G'_3) → driehoek5'_2, g'_3, o'_2, c'_2
  70. Rotate(O, (((s - 5) * 180))°, c_3) → O'_3
  71. Rotate(G, (((s - 5) * 180))°, c_3) → G'_4
  72. Rotate(O'_2, (((-(s - 6)) * 180))°, c'_2) → Q
  73. Rotate(G'_3, (((-(s - 6)) * 180))°, c'_2) → U
  74. Intersect(c', o_1) → V
  75. Intersect(c', o_1) → W
  76. Intersect(c', o_1) → Z
  77. Line(I, H) → r_1
  78. Intersect(o_1, r_1) → T
  79. Segment(O, C) → s_1
  80. Segment(C, G) → t_1
  81. Polygon(I, A, O, T) → vierhoek2, i_5, a_4, o_2, t_2
  82. Rotate(I, (((-(s - 7)) * 180))°, t_2) → I'_1
  83. Rotate(A, (((-(s - 7)) * 180))°, t_2) → A'
  84. Rotate(O, (((-(s - 7)) * 180))°, t_2) → O'_4
  85. Rotate(T, (((-(s - 7)) * 180))°, t_2) → T'
  86. Polygon(I, T, G, E) → vierhoek3, i_6, t_3, g_7, e_8
  87. Segment(E, T) → f_2
  88. Segment(T, E) → j_2
  89. Intersect(Segment[O, N], j_2) → A_1
  90. Segment(A_1, E) → k_2
  91. Rotate(I, (((-(s - 7)) * 180))°, i_6) → I'_2
  92. Rotate(A, (((-(s - 7)) * 180))°, i_6) → A'_1
  93. Rotate(O, (((-(s - 7)) * 180))°, i_6) → O'_5
  94. Rotate(T, (((-(s - 7)) * 180))°, i_6) → T'_1
  95. Polygon(I'_2, A'_1, O'_5, T'_1) → vierhoek2', i'_2, a'_1, o'_5, t'_1
  96. Mirror(N, g) → NN
  97. CircleArc(I, A, NN) → d_2
  98. Segment(I, T) → l_2
  99. Intersect(g'_2, l_2) → B_1
  100. Polygon(N, B_1, T, G) → vierhoek4, n_2, b_3, t_4, g_8
  101. Segment(I, A) → m_2
  102. Segment(A, O) → p_2