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Explore Parallelogram

Explore Parallelogram
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2016-05-10 20:23
PolygonVectorGeometric Construction
This example demonstrates the properties of a parallelogram and its variations, including rectangles, rhombuses, and squares. Using GeoGebra commands such as Line, Intersect, Polygon, etc., the construction process of a parallelogram is visually illustrated. Suitable for middle school and above students and teachers to understand geometric transformations and similar triangles.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Line(A, C) → b
  3. Line(C, a) → c
  4. Line(B, b) → d
  5. Intersect(c, d) → D
  6. OrthogonalLine(C, a) → e
  7. OrthogonalLine(D, a) → f
  8. Polygon(C, A, B, D) → poly1, c_1, a_1, b_1, d_1
  9. Segment(A, D) → g
  10. Segment(B, C) → h
  11. Intersect(g, h) → E
  12. Circle(E, C) → k
  13. Circle(E, D) → p
  14. OrthogonalLine(E, h) → i
  15. OrthogonalLine(E, g) → j
  16. Segment(A, E) → l
  17. Segment(E, D) → m
  18. Segment(E, B) → n
  19. Segment(E, C) → q
  20. Segment(A, E) → r
  21. Segment(E, D) → s
  22. Angle(C, D, B) → α
  23. Angle(D, B, A) → β
  24. Angle(B, A, C) → γ
  25. Angle(A, C, D) → δ
  26. Circle(A, ray) → t
  27. Intersect(t, b, 2) → F
  28. Intersect(t, a, 2) → G
  29. Vector(A, F) → u
  30. Translate(G, u) → G'
  31. Polygon(A, G, G', F) → poly2, a_2, g_1, g', f_1
  32. Vector(F, C) → v
  33. Vector(G, B) → w
  34. Translate(A, v) → A'
  35. Translate(G, v) → G'_1
  36. Translate(G', v) → G''
  37. Translate(F, v) → F'
  38. Polygon(A', G'_1, G'', F') → poly2', a', g'_1, g'', f'
  39. Translate(A, w) → A'_1
  40. Translate(G, w) → G'_2
  41. Translate(G', w) → G''_1
  42. Translate(F, w) → F'_1
  43. Polygon(A'_1, G'_2, G''_1, F'_1) → poly2'_1, a'_1, g'_2, g''_1, f'_1
  44. Translate(A', w) → A''
  45. Translate(G'_1, w) → H
  46. Translate(G'', w) → G'''
  47. Translate(F', w) → F''
  48. Polygon(A'', H, G''', F'') → poly2'', a'', h_1, g''', f''
  49. Vector(G'_2, F') → u_1
  50. Translate(H, u_1) → H'
  51. Segment(C, A) → e_1
  52. Segment(B, D) → i_1
  53. OrthogonalLine(A, c_1) → l_1
  54. Circle(B, D) → q_1

AI Drawing Prompt Reference

Draw a parallelogram by connecting points A, B, C, and D. Then construct the intersection point E of the diagonals, draw circles centered at E, and create parallel lines and vectors. Finally, generate variations of rectangles, rhombuses, and squares through translations.
The prompt above was compiled from the original drawing commands and is for reference only.