Quadrilateral - Can You Draw It?

Quadrilateral - Can You Draw It?
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2017-10-30 08:40
In collections Elementary Geometry
This example demonstrates how to draw quadrilaterals using GeoGebra. Key mathematical concepts include the classification of quadrilaterals (kite, parallelogram, rectangle, rhombus, square) and geometric construction. Using commands like Polygon, Point, Intersect, and Mirror, various quadrilaterals can be constructed. Suitable for middle school and above students or teachers.

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

AI Drawing Prompt Reference

Draw a heptagon, then draw a 1° arc at each vertex, find the intersection points of these arcs, and connect these points to form a new polygon. Next, draw a rectangle, then draw a perpendicular line on one of its diagonals, find the intersection points of this line with the rectangle's sides, and connect these points to form another new polygon. Finally, mirror one of the polygons over another line to form a mirrored polygon.
The prompt above was compiled from the original drawing commands and is for reference only.