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Dyme - 2.5 Dimensional Geometric Construction

Dyme - 2.5 Dimensional Geometric Construction
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2019-10-04 22:16
PolygonFunctionCoordinate GeometryGeometric Construction
This example demonstrates complex geometric construction and property exploration based on geometric drawing; Core math concepts include area calculation, roots, quadratic equations, rhombus properties, intersection solving, and equation applications; Construction highlights are derived from GeoGebra commands: point, orthogonal line, intersect, line, segment, polygon, etc.; Suitable for high school and above learners to understand the correlation between geometric construction and algebraic equations.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. OrthogonalLine(B, yAxis) → f
  3. OrthogonalLine(A, xAxis) → g
  4. Intersect(f, yAxis) → C
  5. Intersect(xAxis, yAxis) → D
  6. Line(C, D) → h
  7. Segment(A, D) → i
  8. Segment(B, C) → j
  9. Segment(B, A) → k
  10. Segment(C, D) → l
  11. Intersect(j, k) → E
  12. Intersect(i, k) → F
  13. Intersect(i, l) → G
  14. Intersect(j, l) → H
  15. Polygon(E, F, G, H) → q1, e, f_1, g_1, h_1
  16. Intersect(i, k) → I
  17. OrthogonalLine(I, j) → m
  18. Intersect(m, j) → J
  19. Point(j) → K
  20. OrthogonalLine(K, i) → n
  21. Intersect(n, i) → L
  22. Segment(K, L) → p
  23. OrthogonalLine(N, xAxis) → q
  24. OrthogonalLine(N, yAxis) → r
  25. Point(r) → M
  26. OrthogonalLine(M, xAxis) → s
  27. Intersect(s, xAxis) → O
  28. OrthogonalLine(O, q) → t
  29. Intersect(q, t) → P
  30. Segment(N, M) → a
  31. Segment(M, O) → b
  32. Segment(O, P) → c
  33. Segment(P, N) → d
  34. Polygon(N, P, O, M) → q2, n_1, p_1, o, m_1
  35. Intersect(c, d) → Q
  36. Point(d) → R
  37. OrthogonalLine(Q, xAxis) → i_1
  38. OrthogonalLine(R, b) → j_1
  39. Intersect(b, c) → S
  40. OrthogonalLine(S, j_1) → k_1
  41. Point(d) → V
  42. OrthogonalLine(V, xAxis) → r_1
  43. Point(d) → W
  44. OrthogonalLine(W, b) → s_1
  45. Intersect(b, o) → Z
  46. Intersect(s_1, b) → A_1
  47. OrthogonalLine(A_1, xAxis) → t_1
  48. Intersect(t_1, b) → B_1
  49. Intersect(t_1, b) → C_1
  50. Intersect(t_1, b) → D_1
  51. Intersect(t_1, b) → E_1
  52. Intersect(t_1, b) → F_1
  53. Intersect(t_1, b) → G_1
  54. Intersect(t_1, b) → H_1
  55. Point(q2) → I_1
  56. OrthogonalLine(I_1, d) → a_1
  57. Polygon(W, V, I_1, A_1) → q3, w, v, b_1, c_1
  58. Point(c_1) → J_1
  59. OrthogonalLine(J_1, a_1) → d_1
  60. Intersect(a_1, d_1) → K_1
  61. Segment(J_1, K_1) → e_1
  62. Intersect(a, d) → L_1
  63. OrthogonalLine(L_1, xAxis) → f_2
  64. Intersect(f_2, d) → M_1
  65. Point(d) → N_1
  66. OrthogonalLine(N_1, b) → g_2
  67. Intersect(b, o) → O_1
  68. Intersect(b, o) → P_1
  69. Point(b) → Q_1
  70. OrthogonalLine(Q_1, xAxis) → h_2
  71. Point(h_2) → R_1
  72. OrthogonalLine(R_1, yAxis) → i_2
  73. Polygon(L_1, N_1, Q_1, R_1) → q4, j_2, k_2, l_2, m_2
  74. Point(a) → S_1
  75. OrthogonalLine(S_1, xAxis) → n_2
  76. Intersect(g_2, n_2) → T_1
  77. Segment(S_1, T_1) → p_2
  78. Point(d) → U_1
  79. Intersect(c, d) → V_1
  80. Point(c) → W_1
  81. Point(b) → Z_1
  82. Polygon(U_1, V_1, W_1, Z_1) → q5, u_1, v_1, w_1, z_1
  83. Point(z_1) → T
  84. OrthogonalLine(T, xAxis) → l_1
  85. Intersect(l_1, c) → U
  86. Segment(T, U) → q_1
  87. Intersect(a, d) → A_2
  88. Intersect(c, d) → B_2
  89. Intersect(b, c) → C_2
  90. Intersect(a, b) → D_2
  91. Polygon(A_2, B_2, C_2, D_2) → q6, a_2, b_2, c_2, d_2