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Line Symmetry Construction

Line Symmetry Construction
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2016-04-05 20:33
PolygonTransformationGeometric Construction
This example demonstrates the construction and analysis of line-symmetric figures. It visually illustrates the relationship between the axis of symmetry and symmetric points by constructing points A, B, and polygon poly1. Key mathematical concepts include symmetry, geometric construction, and polygon formation. GeoGebra commands like Polygon and Segment are used, with auxiliary points C, D, E, F, etc., to complete the figure. Suitable for middle school and high school students learning geometric transformations, symmetry principles, and construction techniques, as well as high school mathematics instruction.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 6) → poly1, a, F, b, c, d, e, f, C, D, E
  2. Polygon(G, H, 3) → poly2, g, h, i, I
  3. Polygon(J, K, 5) → poly3, j, k, l, m, n, L, M, N
  4. Segment(O, P) → p
  5. Segment(P, Q) → q
  6. Segment(O, R) → r
  7. Segment(R, S) → s
  8. Segment(S, T) → t
  9. Segment(T, U) → a_1
  10. Segment(U, V) → b_1
  11. Segment(V, W) → c_1
  12. Segment(W, Z) → d_1
  13. Segment(Z, A_1) → e_1
  14. Segment(A_1, B_1) → f_1
  15. Segment(B_1, Q) → g_1
  16. Segment(C_1, D_1) → h_1
  17. Segment(D_1, C_1) → i_1
  18. Segment(E_1, F_1) → j_1
  19. Segment(G_1, H_1) → k_1
  20. Segment(I_1, J_1) → l_1
  21. Polygon(K_1, L_1, 4) → poly4, m_1, n_1, p_1, q_1, M_1, N_1
  22. Segment(O_1, P_1) → r_1