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Rhombus Conjecture

Rhombus Conjecture
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2016-11-15 22:22
PolygonAngleTrigonometryGeometric Construction
This example illustrates the properties and conjectures of a rhombus. Key mathematical concepts include angles, distances, and polygons. Using GeoGebra commands such as Circle, Intersect, and Polygon, a rhombus can be constructed and its properties explored. Suitable for middle school and above students or teachers.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Circle(B, A) → d
  3. Intersect(c, d, 1) → C
  4. Circle(C, B) → e
  5. Intersect(d, e, 2) → D
  6. Polygon(A, C, D, B) → poly1, a, c_1, d_1, b
  7. Angle(A, C, D) → α
  8. Angle(C, D, B) → β
  9. Angle(D, B, A) → γ
  10. Angle(B, A, C) → δ
  11. Segment(C, B) → f
  12. Segment(D, A) → g
  13. Intersect(f, g) → E
  14. Angle(C, E, A) → ε
  15. Angle(A, E, B) → ζ
  16. Angle(B, E, D) → η
  17. Angle(D, E, C) → θ
  18. Distance(C, D) → distanceCD
  19. Midpoint(C, D) →
  20. Distance(D, B) → distanceDB
  21. Midpoint(D, B) →
  22. Distance(B, A) → distanceBA
  23. Midpoint(B, A) →
  24. Distance(A, C) → distanceAC
  25. Midpoint(A, C) →
  26. Distance(B, E) → distanceBE
  27. Midpoint(B, E) →
  28. Distance(E, D) → distanceED
  29. Midpoint(E, D) →
  30. Distance(E, C) → distanceEC
  31. Midpoint(E, C) →
  32. Distance(E, A) → distanceEA
  33. Midpoint(E, A) →