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Rhombus, Square, Trapezoid Construction

Rhombus, Square, Trapezoid Construction
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2016-03-09 22:11
PolygonCoordinate GeometryGeometric Construction
This example demonstrates the geometric construction and properties of rhombuses, squares, and trapezoids. Key math concepts include polygons, angles, distances, and coordinate geometry. It utilizes GeoGebra commands like Circle, Intersect, Distance, Segment, Angle, Point, OrthogonalLine, and Line. Suitable for high school mathematics education or for geometry enthusiasts.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Circle(B, A) → d
  3. Intersect(c, d, 1) → C
  4. Intersect(c, d, 2) → D
  5. Distance(A, C) → distanceAC
  6. Segment(C, A) → a
  7. Segment(A, D) → b
  8. Segment(C, B) → e
  9. Segment(D, B) → f
  10. Distance(A, C) → g
  11. Distance(B, C) → distanceBC
  12. Distance(D, B) → distanceDB
  13. Distance(D, A) → distanceDA
  14. Angle(A, C, B) → α
  15. Angle(C, B, D) → β
  16. Angle(D, A, C) → ζ
  17. Angle(B, D, A) → δ
  18. Circle(E, 3.4242663447810293) → h
  19. Point(h) → F
  20. Circle(F, 3.490866199484813) → k
  21. Segment(E, F) → i
  22. OrthogonalLine(F, i) → j
  23. Intersect(k, j, 1) → G
  24. OrthogonalLine(E, i) → l
  25. Intersect(h, l, 1) → H
  26. OrthogonalLine(H, j) → m
  27. Distance(E, H) → distanceEH
  28. Distance(F, G) → distanceFG
  29. Distance(E, F) → distanceEF
  30. Distance(G, H) → distanceGH
  31. Angle(j, m) → η
  32. Circle(J, K) → p
  33. Point(p) → I
  34. Segment(J, K) → n
  35. Segment(J, I) → r
  36. Segment(I, K) → s
  37. Distance(I, J) → distanceIJ
  38. Distance(J, K) → distanceJK
  39. Distance(I, K) → distanceIK
  40. Point(n) → M
  41. Line(M, s) → q
  42. Intersect(q, r) → L
  43. Distance(L, I) → distanceLI
  44. Distance(M, K) → distanceMK
  45. Distance(L, M) → distanceLM
  46. Distance(I, K) → o