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Divide a Line Segment into Equal Parts

Divide a Line Segment into Equal Parts
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2014-03-06 03:39
CircleTransformationGeometric Construction
In collections Introduction to Geometry
This example demonstrates how to divide a line segment into 3, 4, or 5 equal parts. Through a dynamic diagram, students can intuitively understand the basic principles of geometric construction. Key mathematical concepts include geometric construction, line segment division, and geometric transformations. GeoGebra commands used include Circle, Ray, OrthogonalLine, Intersect, Segment, Line, and CircleArc. Suitable for middle school and above students to learn geometric construction.

GeoGebra Commands & Parameters

  1. Circle(C, 0.55) → e_1
  2. Ray(A, C) → b
  3. OrthogonalLine(C, b) → i
  4. Intersect(e_1, i) → P, Q
  5. Segment(A, B) → a
  6. Line(Q, b) → f
  7. Line(P, b) → e
  8. Circle(A, Radius) → g
  9. Circle(A, (2 * Radius)) → h
  10. Circle(A, (3 * Radius)) → k
  11. Circle(A, (4 * Radius)) → p
  12. Circle(A, (5 * Radius)) → q
  13. Intersect(g, f, 2) → F
  14. Intersect(g, e, 2) → G
  15. Intersect(h, f, 2) → H
  16. Intersect(h, e, 2) → I
  17. Intersect(k, f, 2) → J
  18. Intersect(k, e, 2) → K
  19. Intersect(p, f, 2) → L
  20. Intersect(p, e, 2) → M
  21. Intersect(q, f, 2) → N
  22. Intersect(q, e, 2) → O
  23. CircleArc(A, G, F) → r
  24. CircleArc(A, I, H) → s
  25. CircleArc(A, K, J) → t
  26. CircleArc(A, M, L) → c_1
  27. CircleArc(A, O, N) → d_1
  28. Intersect(r, b, 1) → R
  29. Intersect(s, b, 1) → S
  30. Intersect(t, b, 1) → T
  31. Intersect(c_1, b, 1) → U
  32. Intersect(d_1, b) → V,
  33. Segment(V, B) → j
  34. Line(U, j) → l
  35. Line(T, j) → m
  36. Line(S, j) → n
  37. Line(R, j) → a_1
  38. Intersect(l, a) → W
  39. Segment(U, W) → b_1
  40. Intersect(m, a) → Z
  41. Segment(T, Z) → f_1
  42. Intersect(n, a) → A_1
  43. Segment(S, A_1) → g_1
  44. Intersect(a_1, a) → B_1
  45. Segment(R, B_1) → h_1
  46. Segment(U, B) → i_1
  47. Line(T, i_1) → j_1
  48. Line(S, i_1) → k_1
  49. Line(R, i_1) → l_1
  50. Intersect(l_1, a) → C_1
  51. Intersect(k_1, a) → D_1
  52. Intersect(j_1, a) → E_1
  53. Segment(T, E_1) → m_1
  54. Segment(S, D_1) → n_1
  55. Segment(R, C_1) → p_1
  56. Segment(T, B) → q_1
  57. Line(S, q_1) → r_1
  58. Line(R, r_1) → s_1
  59. Intersect(s_1, a) → F_1
  60. Intersect(r_1, a) → G_1
  61. Segment(R, F_1) → t_1
  62. Segment(S, G_1) → a_2
  63. CircleArc(A, M, L) → c_2