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Construction of Squares and Rhombi

Construction of Squares and Rhombi
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2014-12-16 14:05
PolygonVectorGeometric Construction
In collections Properties of Parallelograms
This example demonstrates how to construct squares and rhombi using GeoGebra. Key mathematical concepts include geometric construction, vectors, and transformations. Commands such as Line, Rotate, Vector, Translate are used to create these shapes. Suitable for middle school and above students to learn geometric construction and transformations.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Rotate(B, -90*°, A) → D
  3. Vector(A, D) → u
  4. Translate(a, u) → a'
  5. OrthogonalLine(B, a') → b
  6. Intersect(a', b) → C
  7. Polygon(A, B, C, D) → poly1, a_1, b_1, c, b'
  8. Segment(E, G) → d
  9. LineBisector(d) → e
  10. Point(e) → H
  11. Line(E, H) → f
  12. Line(G, H) → g
  13. Mirror(H, d) → F
  14. Polygon(E, F, G, H) → poly2, e_1, g', f_1, g_1
  15. Angle(A, B, C) → α
  16. Angle(C, D, A) → β
  17. Angle(D, A, B) → γ
  18. Angle(B, C, D) → δ
  19. Angle(H, E, F) → ε
  20. Angle(F, G, H) → ζ
  21. Angle(G, H, E) → η
  22. Angle(E, F, G) → θ
  23. Distance(A, B) → distanceAB
  24. Midpoint(A, B) →
  25. Distance(B, C) → distanceBC
  26. Midpoint(B, C) →
  27. Distance(C, D) → distanceCD
  28. Midpoint(C, D) →
  29. Distance(D, A) → distanceDA
  30. Midpoint(D, A) →
  31. Distance(E, F) → distanceEF
  32. Midpoint(E, F) →
  33. Distance(F, G) → distanceFG
  34. Midpoint(F, G) →
  35. Distance(G, H) → distanceGH
  36. Midpoint(G, H) →
  37. Distance(H, E) → distanceHE
  38. Midpoint(H, E) →
  39. Segment(A, C) → j
  40. Segment(B, D) → k
  41. Segment(F, H) → l
  42. Intersect(j, k) → I
  43. Intersect(d, l) → J
  44. Distance(A, I) → distanceAI
  45. Midpoint(A, I) →
  46. Distance(B, I) → distanceBI
  47. Midpoint(B, I) →
  48. Distance(C, I) → distanceCI
  49. Midpoint(C, I) →
  50. Distance(D, I) → distanceDI
  51. Midpoint(D, I) →
  52. Distance(E, J) → distanceEJ
  53. Midpoint(E, J) →
  54. Distance(F, J) → distanceFJ
  55. Midpoint(F, J) →
  56. Distance(G, J) → distanceGJ
  57. Midpoint(G, J) →
  58. Distance(H, J) → distanceHJ
  59. Midpoint(H, J) →
  60. Angle(A, I, D) → ι
  61. Angle(E, J, H) → κ

AI Drawing Prompt Reference

Draw a square and a rhombus to demonstrate their geometric construction using line segments and vectors. Start by drawing a line segment, then rotate it 90 degrees around one endpoint to get a second line segment. Represent the direction between these two segments as a vector. Next, translate the first line segment along this vector to obtain the second line segment. Draw a line perpendicular to the translated segment, find the intersection points with the original and translated segments, and connect these points to form the square. For the rhombus, draw a line segment, locate its midpoint, draw a perpendicular bisector, find a point on this bisector, and connect this point to the endpoints of the segment to form the rhombus.
The prompt above was compiled from the original drawing commands and is for reference only.