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Quadrilateral Predictions

Quadrilateral Predictions
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2017-10-30 09:01
CirclePolygonGeometric Construction
In collections Elementary Geometry
This example demonstrates geometric properties and predictions of quadrilaterals. It involves core concepts like polygons, circumcircle, incircle, and prism. Construction uses commands such as Polygon, Point, Intersect, Mirror, OrthogonalLine, Circle. Suitable for high school mathematics education to understand the geometric relationship between quadrilaterals and circles.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  2. Polygon(A_1, B_1, 4) → poly1_1, f_1, g_1, h_1, i_1, C_1, D_1
  3. Polygon(A_2, B_2, 4) → poly1_2, f_2, g_2, h_2, i_2, C_2, D_2
  4. Polygon(A_3, B_3, 4) → poly1_3, f_3, g_3, h_3, i_3, C_3, D_3
  5. Polygon(A_4, B_4, 4) → poly1_4, f_4, g_4, h_4, i_4, C_4, D_4
  6. Polygon(A_5, B_5, 4) → poly1_5, f_5, g_5, h_5, i_5, C_5, D_5
  7. Polygon(A_6, B_6, 4) → poly1_6, f_6, g_6, h_6, i_6, C_6, D_6
  8. Polygon(A_7, B_7, 4) → poly1_7, f_7, g_7, h_7, i_7, C_7, D_7
  9. Point(CircleArc[E, Rotate[F, -1°, E], Rotate[F, (-(179°)), E]]) → G
  10. Intersect(Circle[G, E], Circle[F, E]) → H, I, ,
  11. Polygon(E, F, I, G) → q1, e, f_8, i_8, g_8
  12. Point(CircleArc[E_1, Rotate[F_1, -1°, E_1], Rotate[F_1, (-(179°)), E_1]]) → G_1
  13. Intersect(Circle[G_1, E_1], Circle[F_1, E_1]) → H_1, I_1, ,
  14. Polygon(E_1, F_1, I_1, G_1) → q1_1, e_1, f_9, i_9, g_9
  15. Point(CircleArc[E_2, Rotate[F_2, -1°, E_2], Rotate[F_2, (-(179°)), E_2]]) → G_2
  16. Intersect(Circle[G_2, E_2], Circle[F_2, E_2]) → H_2, I_2, ,
  17. Polygon(E_2, F_2, I_2, G_2) → q1_2, e_2, f_{10}, i_{10}, g_{10}
  18. Point(CircleArc[E_3, Rotate[F_3, -1°, E_3], Rotate[F_3, (-(179°)), E_3]]) → G_3
  19. Intersect(Circle[G_3, E_3], Circle[F_3, E_3]) → H_3, I_3, ,
  20. Polygon(E_3, F_3, I_3, G_3) → q1_3, e_3, f_{11}, i_{11}, g_{11}
  21. Point(CircleArc[E_4, Rotate[F_4, -1°, E_4], Rotate[F_4, (-(179°)), E_4]]) → G_4
  22. Intersect(Circle[G_4, E_4], Circle[F_4, E_4]) → H_4, I_4, ,
  23. Polygon(E_4, F_4, I_4, G_4) → q1_4, e_4, f_{12}, i_{12}, g_{12}
  24. Point(CircleArc[E_5, Rotate[F_5, -1°, E_5], Rotate[F_5, (-(179°)), E_5]]) → G_5
  25. Intersect(Circle[G_5, E_5], Circle[F_5, E_5]) → H_5, I_5, ,
  26. Polygon(E_5, F_5, I_5, G_5) → q1_5, e_5, f_{13}, i_{13}, g_{13}
  27. Point(CircleArc[E_6, Rotate[F_6, -1°, E_6], Rotate[F_6, (-(179°)), E_6]]) → G_6
  28. Intersect(Circle[G_6, E_6], Circle[F_6, E_6]) → H_6, I_6, ,
  29. Polygon(E_6, F_6, I_6, G_6) → q1_6, e_6, f_{14}, i_{14}, g_{14}
  30. Point(CircleArc[E_7, Rotate[F_7, -1°, E_7], Rotate[F_7, (-(179°)), E_7]]) → G_7
  31. Intersect(Circle[G_7, E_7], Circle[F_7, E_7]) → H_7, I_7, ,
  32. Polygon(E_7, F_7, I_7, G_7) → q1_7, e_7, f_{15}, i_{15}, g_{15}
  33. Point(OrthogonalLine[J, Line[J, K]]) → M
  34. Polygon(J, K, N, M) → q2, j, k, n, m
  35. Point(OrthogonalLine[J_1, Line[J_1, K_1]]) → M_1
  36. Polygon(J_1, K_1, N_1, M_1) → q2_1, j_1, k_1, n_1, m_1
  37. Point(OrthogonalLine[J_2, Line[J_2, K_2]]) → M_2
  38. Polygon(J_2, K_2, N_2, M_2) → q2_2, j_2, k_2, n_2, m_2
  39. Point(OrthogonalLine[J_3, Line[J_3, K_3]]) → M_3
  40. Polygon(J_3, K_3, N_3, M_3) → q2_3, j_3, k_3, n_3, m_3
  41. Mirror(Q, Line[O, P]) → Q'
  42. Polygon(O, Q, P, Q') → q3, o, q, p, q'
  43. Mirror(Q_1, Line[O_1, P_1]) → Q'_1
  44. Polygon(O_1, Q_1, P_1, Q'_1) → q3_1, o_1, q_1, p_1, q'_1
  45. Mirror(Q_2, Line[O_2, P_2]) → Q'_2
  46. Polygon(O_2, Q_2, P_2, Q'_2) → q3_2, o_2, q_2, p_2, q'_2
  47. Mirror(Q_3, Line[O_3, P_3]) → Q'_3
  48. Polygon(O_3, Q_3, P_3, Q'_3) → q3_3, o_3, q_3, p_3, q'_3
  49. Polygon(S, U, T, R) → q4, s, u, t, r
  50. Polygon(S_1, U_1, T_1, R_1) → q4_1, s_1, u_1, t_1, r_1
  51. Polygon(S_2, U_2, T_2, R_2) → q4_2, s_2, u_2, t_2, r_2
  52. Polygon(S_3, U_3, T_3, R_3) → q4_3, s_3, u_3, t_3, r_3
  53. Point(Ray[Z, Z + W - V]) → L_1
  54. Polygon(V, W, L_1, Z) → q5, v, w, l_1, z_1
  55. Point(Ray[Z_1, Z_1 + W_1 - V_1]) → L_2
  56. Polygon(V_1, W_1, L_2, Z_1) → q5_1, v_1, w_1, l_2, z_2
  57. Point(Ray[Z_2, Z_2 + W_2 - V_2]) → L_3
  58. Polygon(V_2, W_2, L_3, Z_2) → q5_2, v_2, w_2, l_3, z_3
  59. Point(Ray[Z_3, Z_3 + W_3 - V_3]) → L_4
  60. Polygon(V_3, W_3, L_4, Z_3) → q5_3, v_3, w_3, l_4, z_4
  61. Polygon(J_4, K_4, M_4, N_4) → q6, j_4, k_4, m_4, n_4
  62. Polygon(J_5, K_5, M_5, N_5) → q6_1, j_5, k_5, m_5, n_5
  63. Polygon(J_6, K_6, M_6, N_6) → q6_2, j_6, k_6, m_6, n_6
  64. Polygon(J_7, K_7, M_7, N_7) → q6_3, j_7, k_7, m_7, n_7
  65. OrthogonalLine(P_4, Line[O_4, P_4]) → l
  66. Point(l) → Q_4
  67. OrthogonalLine(O_4, Line[O_4, P_4]) → a
  68. Point(a) → R_4
  69. Polygon(O_4, P_4, Q_4, R_4) → q7, o_4, p_4, q_4, r_4
  70. Polygon(U_4, T_4, V_4, S_4) → q8, u_4, t_4, v_4, s_4
  71. Circle(W_4, Z_4) → c
  72. Point(c) → L_5
  73. Circle(L_5, W_4) → d
  74. Circle(Z_4, W_4) → c_1
  75. Intersect(d, c_1, 2) → O_5
  76. Polygon(L_5, O_5, Z_4, W_4) → q9, l_5, o_5, z_5, w_4
  77. Polygon(P_5, Q_5, 4) → poly2, b, a_1, b_1, d_1, R_5, S_5
  78. Point(Ray[U_5, Rotate[T_5, (-(90°)), U_5]]) → V_5
  79. Polygon(T_5, U_5, V_5, W_5) → q10, t_5, u_5, v_5, w_5