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Rotational Symmetry by MiGunning03

Rotational Symmetry by MiGunning03
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2018-01-16 23:25
PolygonTransformationGeometric Construction
This example demonstrates the construction of rotationally symmetric figures. Key mathematical concepts include rotational symmetry and geometric construction. Using GeoGebra commands such as Rotate, Angle, and Polygon, rotationally symmetric polygons can be constructed. Suitable for middle school and above students to learn about rotational symmetry and its applications.

GeoGebra Commands & Parameters

  1. Line(Q_1, P_1) → f_3
  2. Polygon(P_1, Q_1, 5) → poly7, l_2, m_2, n_2, p_2, q_2, R_1, S_1, T_1
  3. Line(R_1, Q_1) → h_3
  4. Intersect(h_3, f_3) → D_2
  5. Line(S_1, T_1) → t_2
  6. Intersect(t_2, f_3) → V_1
  7. Line(R_1, S_1) → s_2
  8. Line(P_1, T_1) → r_2
  9. Intersect(s_2, r_2) → U_1
  10. Segment(U_1, D_2) → k_3
  11. Mirror(V_1, k_3) → U_2
  12. Segment(A, B) → a
  13. OrthogonalLine(A, a) → b
  14. OrthogonalLine(B, a) → c
  15. Point(b) → C
  16. OrthogonalLine(C, b) → d
  17. Intersect(c, d) → D
  18. Polygon(C, D, B, A) → poly1, c_1, d_1, b_1, a_1
  19. Segment(C, B) → e
  20. Segment(D, A) → f
  21. Intersect(e, f) → E
  22. Polygon(F, G, 4) → poly2, f_1, g, h, i, H, I
  23. Segment(I, G) → j
  24. Segment(H, F) → k
  25. Intersect(j, k) → J
  26. Segment(K, L) → l
  27. Circle(K, L) → p
  28. Point(p) → M
  29. Segment(K, M) → m
  30. Line(M, l) → n
  31. Line(L, m) → q
  32. Intersect(n, q) → N
  33. Segment(M, L) → r
  34. Segment(N, K) → s
  35. Intersect(r, s) → O
  36. Polygon(M, N, L, K) → poly3, m_1, n_1, l_1, k_1
  37. Rotate(C, (-α), E) → C'
  38. Rotate(D, (-α), E) → D'
  39. Rotate(B, (-α), E) → B'
  40. Rotate(A, (-α), E) → A'
  41. Polygon(C', D', B', A') → Rectangle, c', d', b', a'
  42. Rotate(M, (-α), O) → M'
  43. Rotate(N, (-α), O) → N'
  44. Rotate(L, (-α), O) → L'
  45. Rotate(K, (-α), O) → K'
  46. Polygon(M', N', L', K') → Rhombus, m', n', l', k'
  47. Segment(P, Q) → t
  48. Segment(P, R) → e_1
  49. Line(Q, e_1) → g_1
  50. Line(R, t) → h_1
  51. Intersect(g_1, h_1) → S
  52. Polygon(P, R, S, Q) → poly4, p_1, r_1, s_1, q_1
  53. Segment(R, Q) → i_1
  54. Segment(S, P) → j_1
  55. Intersect(i_1, j_1) → T
  56. Rotate(P, (-α), T) → P'
  57. Rotate(R, (-α), T) → R'
  58. Rotate(S, (-α), T) → S'
  59. Rotate(Q, (-α), T) → Q'
  60. Polygon(P', R', S', Q') → Parallelogram, p', r', s', q'
  61. Segment(U, V) → t_1
  62. Segment(U, W) → a_2
  63. Line(W, t_1) → b_2
  64. Point(b_2) → Z
  65. Segment(Z, V) → c_2
  66. Polygon(U, V, Z, W) → poly5, u, v, z, w
  67. Segment(W, V) → d_2
  68. Segment(Z, U) → e_2
  69. Intersect(d_2, e_2) → A_1
  70. Rotate(U, (-α), A_1) → U'
  71. Rotate(V, (-α), A_1) → V'
  72. Rotate(Z, (-α), A_1) → Z'
  73. Rotate(W, (-α), A_1) → W'
  74. Polygon(U', V', Z', W') → Trapezoid, u', v', z', w'
  75. Line(B_1, C_1) → f_2
  76. Mirror(D_1, f_2) → E_1
  77. Polygon(D_1, B_1, E_1, C_1) → poly6, d_3, b_3, e_3, c_3
  78. Segment(D_1, E_1) → g_2
  79. Intersect(f_2, g_2) → F_1
  80. Rotate(D_1, (-α), F_1) → G_1
  81. Rotate(B_1, (-α), F_1) → H_1
  82. Rotate(E_1, (-α), F_1) → I_1
  83. Rotate(C_1, (-α), F_1) → J_1
  84. Polygon(G_1, H_1, I_1, J_1) → Kite, g_3, h_2, i_2, j_2
  85. Rotate(poly2, (-α), J) → Square
  86. Line(K_1, L_1) → k_2
  87. Circle(M_1, N_1) → Circle
  88. Rotate(N_1, α, M_1) → O_1
  89. Angle(N_1, M_1, O_1) → β
  90. Intersect(r_2, h_3) → W_1
  91. Intersect(f_3, s_2) → Z_1
  92. Intersect(h_3, t_2) → A_2
  93. Intersect(r_2, t_2) → B_2
  94. Intersect(f_3, r_2) → C_2
  95. Intersect(s_2, h_3) → E_2
  96. Intersect(s_2, t_2) → F_2
  97. Polygon(U_1, B_2, V_1, C_2, W_1, D_2, Z_1, E_2, G_2, F_2) → poly8, u_1, f_4, b_4, v_1, c_4, w_1, d_4, z_1, e_4, g_4
  98. Line(H_2, I_2) → i_3
  99. Mirror(J_2, i_3) → O_2
  100. Mirror(K_2, i_3) → P_2
  101. Mirror(L_2, i_3) → Q_2
  102. Mirror(M_2, i_3) → R_2
  103. Mirror(N_2, i_3) → S_2
  104. Polygon(J_2, O_2, P_2, Q_2, R_2, S_2, N_2, M_2, L_2, T_2) → poly9, j_3, t_3, o_2, p_3, q_3, r_3, s_3, n_3, m_3, l_3