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Symmetry Lines of the Letter H

Symmetry Lines of the Letter H
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2013-08-03 01:35
TransformationGeometric Construction
This example investigates the lines of symmetry of the letter H. Key math concepts include symmetry. Construction highlights include using GeoGebra commands for lines, arcs, and rotations. Suitable for middle school geometry students.

GeoGebra Commands & Parameters

  1. Segment(A1, B) → a_3
  2. OrthogonalLine(A1, a_3) → b
  3. OrthogonalLine(B, a_3) → c
  4. Line(A1, B) → d
  5. Circle(B, A1) → e
  6. Intersect(e, d, 2) → C
  7. Circle(C, B) → f
  8. Intersect(f, d, 2) → D
  9. OrthogonalLine(C, d) → g
  10. OrthogonalLine(D, d) → h
  11. Intersect(e, c, 1) → E
  12. Intersect(f, g, 1) → F
  13. Circle(E, B) → k
  14. Intersect(k, c) → G, H
  15. Circle(H, E) → p
  16. Intersect(p, c, 2) → I
  17. OrthogonalLine(I, c) → i
  18. OrthogonalLine(H, c) → j
  19. Intersect(b, i) → J
  20. Intersect(g, i) → K
  21. Intersect(h, i) → L
  22. Intersect(g, j) → M
  23. Midpoint(H, M) → N
  24. Midpoint(E, F) → O
  25. Line(N, O) → l
  26. Point(l) → P
  27. Midpoint(N, O) → Q
  28. Circle(Q, P) → q
  29. Point(q) → R
  30. Point(q) → S
  31. CircumcircleArc(R, P, S) → r
  32. Rotate(i, 45*°, J) → m
  33. Intersect(l, m) → T
  34. Line(I, m) → s
  35. Intersect(l, s) → U
  36. Line(H, s) → n
  37. Line(B, n) → t
  38. Intersect(l, n) → V
  39. Intersect(l, t) → W
  40. Vector(J, T) → u
  41. Translate(J, Vector[o * u]) → Y
  42. Vector(T, L) → v
  43. Translate(T, Vector[(o - 1) * v]) → Z
  44. Vector(I, U) → w
  45. Vector(U, K) → z
  46. Point(r) → A
  47. Line(Q, A) → a
  48. If(o ≤ 1, Y, Z) → B_1
  49. If(c_1 < b_1, J, B_1) → C_1
  50. Translate(I, Vector[o * w]) → D_1
  51. Translate(H, Vector[o * w]) → E_1
  52. Translate(E, Vector[o * w]) → F_1
  53. Translate(G, Vector[o * w]) → G_1
  54. Translate(U, Vector[(o - 1) * z]) → H_1
  55. Translate(V, Vector[(o - 1) * z]) → I_1
  56. Translate(Q, Vector[(o - 1) * z]) → J_1
  57. Translate(W, Vector[(o - 1) * z]) → K_1
  58. If(o ≤ 1, D_1, H_1) → L_1
  59. If(o ≤ 1, E_1, I_1) → M_1
  60. If(o ≤ 1, F_1, J_1) → N_1
  61. If(o ≤ 1, G_1, K_1) → O_1
  62. Translate(Q, Vector[(o - 1) * u]) → P_1
  63. Translate(Q, Vector[(o - 1) * v]) → Q_1
  64. If(o ≤ 1, P_1, Q_1) → R_1
  65. If(c_1 < b_1, I, L_1) → S_1
  66. If(c_1 < b_1, H, M_1) → T_1
  67. If(c_1 < b_1, E, N_1) → U_1
  68. If(c_1 < b_1, G, O_1) → V_1
  69. If(c_1 < b_1, A1, R_1) → W_1
  70. Polygon(L, D, C, F, O, N, M, K) → Y_1, l_1, d_1, c_2, f_1, o_1, n_1, m_1, k_1
  71. Polygon(C_1, S_1, T_1, N, O, U_1, V_1, W_1) → Z_1, c_3, s_1, t_1, n_2, o_2, u_1, v_1, w_1
  72. Polygon(J, A1, G, E, O, N, H, I) → P_2, j_1, a_2, g_1, e_1, o_3, n_3, h_1, i_1

AI Drawing Prompt Reference

Draw the symmetry lines of the letter H. Start by drawing the two vertical lines of H, then construct perpendicular lines from these vertical lines to find their intersections with H. Use these intersection points to construct the symmetry lines. Finally, apply rotations and translations to ensure all symmetry lines are correctly aligned.
The prompt above was compiled from the original drawing commands and is for reference only.