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Rotation and Reflectional Symmetry of Regular Polygon

Rotation and Reflectional Symmetry of Regular Polygon
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2018-03-20 10:17
PolygonTransformationGeometric Construction
This example demonstrates the rotation and reflectional symmetry of regular polygons. It involves core mathematical concepts such as symmetry, rotation angles, reflection axes, and geometric transformations. The construction uses GeoGebra commands and objects like Polygon, Midpoint, OrthogonalLine, Intersect, Line, and Rotate. It is suitable for high school students learning about geometric transformations and symmetry.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 12) → poly1, f, p, q, r, C, D, E, F, G, H, I, g, J, K, L, h, i, j, k, l, m, n
  2. Midpoint(A, B) → M
  3. OrthogonalLine(M, f) → s
  4. Midpoint(E, D) → N
  5. OrthogonalLine(N, i) → t
  6. Intersect(s, t) → O
  7. Line(F, L) → a
  8. Rotate(A, (-α), O) → A'
  9. Rotate(B, (-α), O) → B'
  10. Polygon(A', B', 12) → poly2, b, k_1, l_1, m_1, P, Q, R, S, T, U, V, c, W, Z, A_1, d, e, f_1, g_1, h_1, i_1, j_1
  11. Polygon(B_1, C_1, 9) → poly3, n_1, D_1, E_1, F_1, G_1, H_1, I_1, J_1, p_1, q_1, r_1, s_1, t_1, a_1, b_1, c_1
  12. OrthogonalLine(G_1, n_1) → d_1
  13. OrthogonalLine(F_1, c_1) → e_1
  14. Intersect(d_1, e_1) → K_1
  15. Rotate(B_1, (-β), K_1) → L_1
  16. Rotate(C_1, (-β), K_1) → M_1
  17. Polygon(L_1, M_1, 9) → poly4, f_2, N_1, O_1, P_1, Q_1, R_1, S_1, T_1, g_2, h_2, i_2, j_2, k_2, l_2, m_2, n_2
  18. Polygon(U_1, V_1, 10) → poly5, p_2, e_2, W_1, Z_1, A_2, B_2, C_2, D_2, E_2, F_2, q_2, r_2, s_2, t_2, a_2, b_2, c_2, d_2