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Geometric Construction: Unit 5

Geometric Construction: Unit 5
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2017-01-25 02:05
PolygonAngleGeometric Construction
This example demonstrates the construction process in geometry. Key mathematical concepts include segments, circles, intersections, rays, and polygons. Using GeoGebra commands such as Segment, Circle, and Intersect, complex geometric shapes can be constructed. Suitable for students at the junior high school level and above to learn geometric construction techniques.

GeoGebra Commands & Parameters

  1. Segment(H, I) → h
  2. Segment(Q, R) → m
  3. Segment(R, S) → n
  4. Circle(R, h) → s
  5. Intersect(s, m, 1) → T
  6. Intersect(s, n, 1) → U
  7. Circle(T, h) → t
  8. Circle(U, h) → c_1
  9. Intersect(t, c_1, 1) → V
  10. Ray(R, V) → a
  11. Polygon(W, Z, A_1) → poly2, a_1, w, z_1
  12. Segment(B_1, C_1) → b
  13. Circle(W, b) → d_1
  14. Circle(Z, b) → e_1
  15. Circle(A_1, b) → h_1
  16. Intersect(e_1, a_1, 1) → D_1
  17. Intersect(e_1, w, 1) → E_1
  18. Intersect(d_1, a_1, 1) → F_1
  19. Intersect(d_1, z_1) → G_1,
  20. Intersect(h_1, z_1, 1) → H_1
  21. Intersect(h_1, w, 1) → I_1
  22. Circle(E_1, b) → k_1
  23. Circle(D_1, b) → p_1
  24. Circle(F_1, b) → q_1
  25. Circle(G_1, b) → r_1
  26. Circle(I_1, b) → s_1
  27. Circle(H_1, b) → t_1
  28. Intersect(k_1, p_1, 2) → J_1
  29. Intersect(q_1, r_1, 2) → K_1
  30. Intersect(s_1, t_1, 1) → L_1
  31. Ray(A_1, L_1) → i_1
  32. Ray(Z, J_1) → j_1
  33. Ray(W, K_1) → l_1
  34. Intersect(i_1, j_1) → Incenter
  35. Point(a_1) → N_1
  36. OrthogonalLine(Incenter, w) → m_1
  37. Intersect(m_1, w) → O_1
  38. Circle(Incenter, O_1) → c_2
  39. Segment(P_1, Q_1) → n_1
  40. Circle(P_1, Q_1) → d_2
  41. Circle(Q_1, P_1) → e_2
  42. Intersect(e_2, d_2) → R_1, S_1, ,
  43. Intersect(e_2, d_2, 2) → T_1
  44. Line(R_1, S_1) → b_1
  45. Segment(R_1, T_1) → f_2
  46. Polygon(U_1, V_1, W_1) → poly3, w_1, u_1, v_1
  47. Circle(W_1, U_1) → g_2
  48. Circle(U_1, W_1) → h_2
  49. Circle(W_1, V_1) → k_2
  50. Circle(V_1, W_1) → p_2
  51. Intersect(k_2, p_2, 1) → Z_1
  52. Intersect(k_2, p_2, 2) → A_2
  53. Intersect(g_2, h_2, 2) → B_2
  54. Intersect(g_2, h_2, 1) → C_2
  55. Circle(U_1, V_1) → q_2
  56. Circle(V_1, U_1) → r_2
  57. Intersect(q_2, r_2, 1) → D_2
  58. Intersect(q_2, r_2, 2) → E_2
  59. Angle(n, a) → β
  60. Angle(V, R, Q) → α
  61. Intersect(n_1, f_2) → A
  62. Angle(P_1, A, R_1) → γ
  63. Line(B_2, C_2) → f
  64. Line(E_2, D_2) → g
  65. Line(Z_1, A_2) → i
  66. Intersect(f, g) → Circumcenter
  67. Circle(Circumcenter, U_1) → c
  68. Polygon(C, D, E) → poly1, e, c_3, d
  69. Midpoint(c_3) → F
  70. Midpoint(e) → G
  71. Midpoint(d) → J
  72. Line(C, F) → j
  73. Line(D, J) → k
  74. Line(E, G) → l
  75. Intersect(j, k) → Centroid
  76. Segment(Centroid, C) → p
  77. Segment(D, Centroid) → q
  78. Segment(Centroid, E) → r
  79. Polygon(D, Centroid, E) → poly4, e_3, d_3, k_3
  80. Polygon(C, Centroid, D) → poly5, d_4, c_4, k_4
  81. Polygon(C, E, Centroid) → poly6, k_5, c_5, e_4
  82. PointIn(poly5) → Pointpoly5_1
  83. PointIn(poly4) → Pointpoly4
  84. PointIn(poly6) → Pointpoly6
  85. PointIn(poly5) → Pointpoly5
  86. Polygon(L, M, N) → poly7, n_2, l_2, m_2
  87. Line(L, N) → f_1
  88. Line(N, M) → g_1
  89. Line(L, M) → i_2
  90. OrthogonalLine(N, i_2) → j_2
  91. OrthogonalLine(M, f_1) → s_2
  92. OrthogonalLine(L, g_1) → t_2
  93. Intersect(j_2, s_2) → Orthocenter
  94. Intersect(f_1, s_2) → P
  95. Intersect(g_1, t_2) → F_2
  96. Intersect(i_2, j_2) → G_2