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Sean Jackson Constructions: Comprehensive Geometric Construction with Segments,

Sean Jackson Constructions: Comprehensive Geometric Construction with Segments,
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2016-03-09 23:18
CircleAngleCoordinate GeometryTransformationGeometric Construction
This GeoGebra example presents a complex geometric construction involving points, segments, lines, circles, orthogonal lines, midpoints, and reflections, demonstrating how to build a network of geometric relationships with angle and distance measurements plus text annotations. The core mathematical concepts include Euclidean construction techniques (midpoint, perpendicular, reflection), angle and distance measurement, and potential extensions to linear regression, parametric curves, sine functions, random variables, and spheres. The construction uses GeoGebra commands such as Segment, Line, Point, Intersect, Angle, Distance, Circle, OrthogonalLine, Midpoint, and Mirror, creating numerous objects: points (A, B, C, D, E, F, G, H, I, J, K), segments/lines (a, b, c, d, e, f, h, g, i, j, k, q, l, m, n, p, r), angles (α, β, γ, δ), and distance text labels (distanceAF, TextAF, etc.). Suitable for middle school and above for geometric construction practice, dynamic exploration of properties, or as a teacher demonstration of step-by-step construction.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Line(C, a) → b
  3. Point(b) → D
  4. Segment(B, D) → c
  5. Line(A, c) → d
  6. Intersect(b, d) → E
  7. Segment(D, E) → e
  8. Segment(A, E) → f
  9. Angle(B, A, E) → α
  10. Angle(A, E, D) → β
  11. Angle(E, D, B) → γ
  12. Angle(D, B, A) → δ
  13. Segment(E, B) → h
  14. Segment(A, D) → g
  15. Intersect(h, g) → F
  16. Distance(A, F) → distanceAF
  17. Distance(F, E) → distanceFE
  18. Distance(D, F) → distanceDF
  19. Distance(F, B) → distanceFB
  20. Segment(G, H) → i
  21. Circle(G, H) → k
  22. Point(k) → J
  23. Segment(G, J) → j
  24. Circle(G, H) → q
  25. Line(J, i) → l
  26. Line(H, j) → m
  27. Intersect(l, m) → K
  28. Segment(J, K) → n
  29. Segment(K, H) → p
  30. Segment(H, J) → r
  31. Segment(G, K) → s
  32. Intersect(r, s) → L
  33. Angle(G, L, J) → ε
  34. Angle(K, J, L) → ζ
  35. Angle(L, J, G) → η
  36. Angle(J, G, L) → θ
  37. Angle(L, G, H) → ι
  38. Angle(G, H, L) → κ
  39. Angle(L, H, K) → λ
  40. Angle(H, K, L) → μ
  41. Angle(L, K, J) → ν
  42. Segment(M, N) → t
  43. Line(O, t) → a_1
  44. OrthogonalLine(N, t) → b_1
  45. OrthogonalLine(M, t) → c_1
  46. Intersect(a_1, c_1) → P
  47. Intersect(a_1, b_1) → Q
  48. Segment(N, Q) → d_1
  49. Segment(Q, P) → e_1
  50. Segment(P, M) → f_1
  51. Angle(M, N, Q) → ξ
  52. Angle(N, Q, P) → ο
  53. Angle(Q, P, M) → ρ
  54. Angle(P, M, N) → σ
  55. Segment(N, P) → g_1
  56. Segment(Q, M) → h_1
  57. Segment(R, S) → i_1
  58. Circle(R, S) → k_1
  59. OrthogonalLine(R, i_1) → j_1
  60. Circle(R, S) → p_1
  61. Intersect(p_1, j_1, 1) → T
  62. Line(T, i_1) → l_1
  63. OrthogonalLine(S, i_1) → m_1
  64. Intersect(l_1, m_1) → U
  65. Intersect(j_1, l_1) → V
  66. Segment(V, R) → n_1
  67. Segment(U, S) → q_1
  68. Segment(V, U) → r_1
  69. Segment(R, U) → s_1
  70. Segment(S, V) → t_1
  71. Intersect(s_1, t_1) → W
  72. Angle(U, W, S) → τ
  73. Angle(S, W, R) → υ
  74. Angle(R, W, V) → ϕ
  75. Segment(Z, A_1) → a_2
  76. Line(B_1, a_2) → b_2
  77. Point(b_2) → C_1
  78. Segment(Z, C_1) → c_2
  79. Segment(A_1, B_1) → d_2
  80. Segment(C_1, B_1) → e_2
  81. Midpoint(c_2) → D_1
  82. Midpoint(d_2) → E_1
  83. Segment(D_1, E_1) → f_2
  84. Segment(F_1, G_1) → g_2
  85. Line(H_1, g_2) → h_2
  86. Point(h_2) → I_1
  87. Segment(F_1, I_1) → i_2
  88. Midpoint(g_2) → J_1
  89. OrthogonalLine(J_1, g_2) → j_2
  90. Mirror(F_1, j_2) → K_1
  91. Mirror(I_1, j_2) → L_1
  92. Segment(K_1, L_1) → k_2
  93. Segment(I_1, L_1) → l_2
  94. Segment(P_1, Q_1) → p_2
  95. Midpoint(p_2) → R_1
  96. OrthogonalLine(R_1, p_2) → q_2
  97. Point(q_2) → O_1
  98. Segment(P_1, O_1) → n_2
  99. Mirror(P_1, q_2) → S_1
  100. Mirror(O_1, q_2) → T_1
  101. Segment(S_1, T_1) → r_2
  102. Point(q_2) → U_1
  103. Segment(Q_1, U_1) → s_2
  104. Mirror(Q_1, q_2) → V_1
  105. Mirror(U_1, q_2) → W_1
  106. Segment(V_1, W_1) → t_2
  107. Segment(O_1, U_1) → a_3
  108. Intersect(p_2, a_3) → Z_1
  109. Angle(Q_1, Z_1, O_1) → ψ
  110. Angle(U_1, P_1, O_1) → χ
  111. Angle(O_1, Q_1, U_1) → α_1
  112. Angle(V, R, S) → ω
  113. Angle(S, U, V) → β_1
  114. Angle(W, V, R) → γ_1
  115. Angle(W, S, U) → δ_1
  116. Segment(F_1, L_1) → b_3
  117. Segment(I_1, G_1) → c_3