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Analytical Geometry: Parallelogram Properties and Construction

Analytical Geometry: Parallelogram Properties and Construction
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2015-11-05 22:23
PolygonAngleCoordinate GeometryGeometric Construction
This example demonstrates the geometric properties of a parallelogram within analytical geometry. Core concepts involve vector operations, coordinate relationships, and polygon attributes. Construction utilizes GeoGebra commands such as Segment, Line, Angle, Polygon, and PointIn to define vertices and edges. It is suitable for high school geometry students or educators for interactive classroom demonstrations to visualize parallelogram theorems.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Segment(C, D) → b
  3. Segment(A, C) → c
  4. Segment(B, D) → d
  5. Segment(E, B) → e
  6. Segment(E, D) → f
  7. Segment(E, C) → g
  8. Segment(E, A) → h
  9. Line(A, a) → i
  10. Line(D, i) → j
  11. Line(F, c) → k
  12. Angle(E, D, C) → α
  13. Angle(B, D, E) → β
  14. Angle(E, A, B) → γ
  15. Angle(C, A, E) → δ
  16. Angle(D, C, E) → ε
  17. Angle(A, B, E) → ζ
  18. Angle(E, B, D) → η
  19. Angle(E, C, A) → θ
  20. Segment(C, D) → t
  21. Segment(A, C) → a_1
  22. Segment(B, D) → b_1
  23. Segment(A, B) → c_1
  24. Angle(C, A, B) → κ
  25. Angle(B, D, C) → λ
  26. Angle(A, B, D) → μ
  27. Angle(D, C, A) → ν
  28. Segment(B, A) → d_1
  29. Segment(A, D) → e_1
  30. Segment(D, C) → f_1
  31. Segment(C, A) → h_1
  32. Segment(A, D) → i_1
  33. Segment(D, B) → j_1
  34. Segment(A, C) → l_1
  35. Segment(C, B) → m_1
  36. Segment(B, D) → n_1
  37. Segment(A, B) → p_1
  38. Segment(B, C) → q_1
  39. Segment(C, D) → r_1
  40. Segment(A, B) → a_2
  41. Segment(A, C) → b_2
  42. Segment(C, D) → c_2
  43. Segment(D, B) → d_2
  44. Polygon(A, B, D) → poly1, d_3, a_3, b_3
  45. PointIn(poly1) → Pointpoly1
  46. Polygon(A, C, D) → poly2, d_4, a_4, c_3
  47. PointIn(poly2) → Pointpoly2
  48. Polygon(A, C, B) → poly3, b_4, a_5, c_4
  49. Polygon(B, D, C) → poly4, c_5, b_5, d_5
  50. PointIn(poly3) → Pointpoly3
  51. PointIn(poly4) → Pointpoly4