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Rotational Symmetry of Quadrilaterals by Mike Patterson

Rotational Symmetry of Quadrilaterals by Mike Patterson
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2016-06-28 10:16
PolygonTransformationGeometric Construction
This example demonstrates the rotational symmetry of quadrilaterals. Key math concepts include symmetry, rotation angles, and geometric transformations. Construction involves commands like Segment, OrthogonalLine, Point, Intersect, Polygon, Circle, Line, Rotate, and Mirror. Suitable for middle school students and beyond for learning geometric transformations and symmetry, or for classroom demonstrations.

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'

AI Drawing Prompt Reference

Draw a quadrilateral and rotate it by a fixed angle (e.g., negative alpha) about the intersection point of its diagonals, showing both the original and rotated shapes in different colors or line styles. Then draw another quadrilateral, rotate it similarly about its diagonal intersection, and label the rotation angle. Finally, construct a closed four-sided polygon and rotate it about its diagonal intersection to demonstrate rotational symmetry. Clearly mark all rotation centers and angles, ensuring accurate geometric relationships.
The prompt above was compiled from the original drawing commands and is for reference only.