Quadrilateral Exploration by Alan

Quadrilateral Exploration by Alan
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2012-01-24 11:36
In collections Understanding Polygons
This example locks quadrilaterals into specific types for students to experiment and discover their properties. Commands used include Polygon, Point, Mirror, Intersect, Segment, Distance, etc. Suitable for middle school and above students for geometric construction and exploration.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → Q, a, b, c, d
  2. Polygon(A_P, B_P, C_P, D_P) → P, a_p, b_p, c_p, d_p
  3. Point(Line[C_T, Line[A_T, B_T]]) → D_T
  4. Polygon(A_T, B_T, C_T, D_T) → T, a_t, b_t, c_t, d_t
  5. Mirror(C_{T_I}, LineBisector[Segment[A_{T_I}, B_{T_I}]]) → D_{T_I}
  6. Polygon(A_{T_I}, B_{T_I}, C_{T_I}, D_{T_I}) → T_I, a_{t_i}, b_{t_i}, c_{t_i}, d_{t_i}
  7. Point(Circle[B_{RH}, Distance[A_{RH}, B_{RH}]]) → C_{RH}
  8. Polygon(A_{RH}, B_{RH}, C_{RH}, D_{RH}) → R_H, a_rh, b_{rh}, c_{rh}, d_{rh}
  9. Point(Circle[B_K, Distance[A_K, B_K]]) → C_K
  10. Point(LineBisector[A_K, C_K]) → D_K
  11. Polygon(A_K, B_K, C_K, D_K) → K, a_k, b_k, c_k, d_k
  12. Point(OrthogonalLine[B_{RE}, Line[A_{RE}, B_{RE}]]) → C_{RE}
  13. Polygon(A_{RE}, B_{RE}, C_{RE}, D_{RE}) → R_E, a_{re}, b_{re}, c_{re}, d_{re}
  14. Polygon(A_S, B_S, C_S, D_S) → S, a_s, b_s, c_s, d_s
  15. Intersect(Segment[A, C], Segment[B, D]) → E
  16. Segment(A, E) → AE
  17. Segment(B, E) → BE
  18. Segment(D, E) → DE
  19. Segment(C, E) → CE
  20. Intersect(Segment[A_P, C_P], Segment[B_P, D_P]) → E_P
  21. Segment(A_P, E_P) → AE_P
  22. Segment(B_P, E_P) → BE_P
  23. Segment(C_P, E_P) → CE_P
  24. Segment(D_P, E_P) → DE_P
  25. Intersect(Segment[A_{RE}, C_{RE}], Segment[B_{RE}, D_{RE}]) → E_{RE}
  26. Segment(A_{RE}, E_{RE}) → AE_{RE}
  27. Segment(B_{RE}, E_{RE}) → BE_{RE}
  28. Segment(C_{RE}, E_{RE}) → CE_{RE}
  29. Segment(D_{RE}, E_{RE}) → DE_{RE}
  30. Intersect(Segment[A_{RH}, C_{RH}], Segment[B_{RH}, D_{RH}]) → E_{RH}
  31. Segment(A_{RH}, E_{RH}) → AE_{RH}
  32. Segment(B_{RH}, E_{RH}) → BE_{RH}
  33. Segment(C_{RH}, E_{RH}) → CE_{RH}
  34. Segment(D_{RH}, E_{RH}) → DE_{RH}
  35. Intersect(Segment[A_S, C_S], Segment[B_S, D_S]) → E_S
  36. Segment(A_S, E_S) → AE_S
  37. Segment(B_S, E_S) → BE_S
  38. Segment(C_S, E_S) → CE_S
  39. Segment(D_S, E_S) → DE_S
  40. Intersect(Segment[A_K, C_K], Segment[B_K, D_K]) → E_K
  41. Segment(A_K, E_K) → AE_K
  42. Segment(B_K, E_K) → BE_K
  43. Segment(C_K, E_K) → CE_K
  44. Segment(D_K, E_K) → DE_K
  45. Intersect(Segment[A_T, C_T], Segment[B_T, D_T]) → E_T
  46. Segment(A_T, E_T) → AE_T
  47. Segment(B_T, E_T) → BE_T
  48. Segment(C_T, E_T) → CE_T
  49. Segment(D_T, E_T) → DE_T
  50. Intersect(Segment[A_{T_I}, C_{T_I}], Segment[B_{T_I}, D_{T_I}]) → E_{T_I}
  51. Segment(A_{T_I}, E_{T_I}) → AE_{T_I}
  52. Segment(B_{T_I}, E_{T_I}) → BE_{T_I}
  53. Segment(C_{T_I}, E_{T_I}) → CE_{T_I}
  54. Segment(D_{T_I}, E_{T_I}) → DE_{T_I}
  55. Distance(AE_S, DE_S) → e
  56. Distance(A_S, E_S) → distanceASES

AI Drawing Prompt Reference

Draw a quadrilateral ABCD and explore its properties. First, draw quadrilateral ABCD, then draw its symmetric figure P. Next, construct a new quadrilateral T at the intersection of its diagonals D_T. Use transformations like reflection, rotation, and translation to explore different types of quadrilaterals and their properties.
The prompt above was compiled from the original drawing commands and is for reference only.