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Rotational Symmetry of Rhombus

Rotational Symmetry of Rhombus
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2019-02-26 07:35
PolygonTransformationGeometric Construction
This example demonstrates the rotational symmetry of quadrilaterals, specifically rhombuses. Key mathematical concepts include rotation symmetry and geometric construction. Using GeoGebra commands such as Segment, OrthogonalLine, Point, Intersect, Circle, Line, Polygon, Rotate, Mirror, etc., the construction of a rhombus and its rotational symmetry is shown. Suitable for middle school and above 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. Segment(C, B) → e
  8. Segment(D, A) → f
  9. Intersect(e, f) → E
  10. Segment(K, L) → l
  11. Circle(K, L) → p
  12. Point(p) → M
  13. Segment(K, M) → m
  14. Line(M, l) → n
  15. Line(L, m) → q
  16. Intersect(n, q) → N
  17. Segment(M, L) → r
  18. Segment(N, K) → s
  19. Intersect(r, s) → O
  20. Polygon(M, N, L, K) → poly3, m_1, n_1, l_1, k_1
  21. Rotate(C, (-α), E) → C'
  22. Rotate(D, (-α), E) → D'
  23. Rotate(B, (-α), E) → B'
  24. Rotate(A, (-α), E) → A'
  25. Polygon(C', D', B', A') → poly1', c', d', b', a'
  26. Rotate(M, (-α), O) → M'
  27. Rotate(N, (-α), O) → N'
  28. Rotate(L, (-α), O) → L'
  29. Rotate(K, (-α), O) → K'
  30. Polygon(M', N', L', K') → poly3', m', n', l', k'
  31. Segment(P, Q) → t
  32. Segment(P, R) → e_1
  33. Line(Q, e_1) → g_1
  34. Line(R, t) → h_1
  35. Intersect(g_1, h_1) → S
  36. Segment(R, Q) → i_1
  37. Segment(S, P) → j_1
  38. Intersect(i_1, j_1) → T
  39. Rotate(P, (-α), T) → P'
  40. Rotate(R, (-α), T) → R'
  41. Rotate(S, (-α), T) → S'
  42. Rotate(Q, (-α), T) → Q'
  43. Polygon(P', R', S', Q') → poly4', p', r', s', q'
  44. Segment(U, V) → t_1
  45. Line(W, t_1) → b_2
  46. Point(b_2) → Z
  47. Segment(W, V) → d_2
  48. Segment(Z, U) → e_2
  49. Intersect(d_2, e_2) → A_1
  50. Rotate(U, (-α), A_1) → U'
  51. Rotate(V, (-α), A_1) → V'
  52. Rotate(Z, (-α), A_1) → Z'
  53. Rotate(W, (-α), A_1) → W'
  54. Polygon(U', V', Z', W') → poly5', u', v', z', w'
  55. Line(B_1, C_1) → f_2
  56. Mirror(D_1, f_2) → E_1
  57. Segment(D_1, E_1) → g_2
  58. Intersect(f_2, g_2) → F_1
  59. Rotate(D_1, (-α), F_1) → G_1
  60. Rotate(B_1, (-α), F_1) → H_1
  61. Rotate(E_1, (-α), F_1) → I_1
  62. Rotate(C_1, (-α), F_1) → J_1
  63. Polygon(G_1, H_1, I_1, J_1) → poly6', g_3, h_2, i_2, j_2
  64. Intersect(m, m_1) → H
  65. Intersect(m', k') → I