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Rotational Symmetry by raffaele.fantasia1

Rotational Symmetry by raffaele.fantasia1
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2017-07-28 06:03
Coordinate GeometryTransformationGeometric Construction
This example demonstrates the construction of rotationally symmetric figures. It involves the core concept of rotational symmetry and uses commands such as Segment, OrthogonalLine, Point, Intersect, Polygon, Circle, Line, Rotate, Mirror in GeoGebra. Suitable for middle school students learning geometric transformations.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. OrthogonalLine(A, a) → b
  3. OrthogonalLine(B, a) → c
  4. Point(b) → C
  5. OrthogonalLine(C, b) → d
  6. Intersect(c, d) → D
  7. Polygon(C, D, B, A) → poly1, c_1, d_1, b_1, a_1
  8. Segment(C, B) → e
  9. Segment(D, A) → f
  10. Intersect(e, f) → E
  11. Polygon(F, G, 4) → poly2, f_1, g, h, i, H, I
  12. Segment(I, G) → j
  13. Segment(H, F) → k
  14. Intersect(j, k) → J
  15. Segment(K, L) → l
  16. Circle(K, L) → p
  17. Point(p) → M
  18. Segment(K, M) → m
  19. Line(M, l) → n
  20. Line(L, m) → q
  21. Intersect(n, q) → N
  22. Segment(M, L) → r
  23. Segment(N, K) → s
  24. Intersect(r, s) → O
  25. Polygon(M, N, L, K) → poly3, m_1, n_1, l_1, k_1
  26. Rotate(C, -α, E) → C'
  27. Rotate(D, -α, E) → D'
  28. Rotate(B, -α, E) → B'
  29. Rotate(A, -α, E) → A'
  30. Polygon(C', D', B', A') → poly1', c', d', b', a'
  31. Rotate(M, -α, O) → M'
  32. Rotate(N, -α, O) → N'
  33. Rotate(L, -α, O) → L'
  34. Rotate(K, -α, O) → K'
  35. Polygon(M', N', L', K') → poly3', m', n', l', k'
  36. Segment(P, Q) → t
  37. Segment(P, R) → e_1
  38. Line(Q, e_1) → g_1
  39. Line(R, t) → h_1
  40. Intersect(g_1, h_1) → S
  41. Polygon(P, R, S, Q) → poly4, p_1, r_1, s_1, q_1
  42. Segment(R, Q) → i_1
  43. Segment(S, P) → j_1
  44. Intersect(i_1, j_1) → T
  45. Rotate(P, -α, T) → P'
  46. Rotate(R, -α, T) → R'
  47. Rotate(S, -α, T) → S'
  48. Rotate(Q, -α, T) → Q'
  49. Polygon(P', R', S', Q') → poly4', p', r', s', q'
  50. Segment(U, V) → t_1
  51. Segment(U, W) → a_2
  52. Line(W, t_1) → b_2
  53. Point(b_2) → Z
  54. Segment(Z, V) → c_2
  55. Polygon(U, V, Z, W) → poly5, u, v, z, w
  56. Segment(W, V) → d_2
  57. Segment(Z, U) → e_2
  58. Intersect(d_2, e_2) → A_1
  59. Rotate(U, -α, A_1) → U'
  60. Rotate(V, -α, A_1) → V'
  61. Rotate(Z, -α, A_1) → Z'
  62. Rotate(W, -α, A_1) → W'
  63. Polygon(U', V', Z', W') → poly5', u', v', z', w'
  64. Line(B_1, C_1) → f_2
  65. Mirror(D_1, f_2) → E_1
  66. Polygon(D_1, B_1, E_1, C_1) → poly6, d_3, b_3, e_3, c_3
  67. Segment(D_1, E_1) → g_2
  68. Intersect(f_2, g_2) → F_1
  69. Rotate(D_1, -α, F_1) → G_1
  70. Rotate(B_1, -α, F_1) → H_1
  71. Rotate(E_1, -α, F_1) → I_1
  72. Rotate(C_1, -α, F_1) → J_1
  73. Polygon(G_1, H_1, I_1, J_1) → poly6', g_3, h_2, i_2, j_2
  74. Rotate(poly2, -α, J) → poly2'