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Investigation of Kites: Diagonals and Angles

Investigation of Kites: Diagonals and Angles
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2015-11-07 03:47
PolygonAngleGeometric Construction
This example examines the diagonals and angles of a kite to discover that the vertex angles are bisected by the diagonal. Key concepts include kite properties and angle bisectors. GeoGebra commands used include Segment, Point, Angle, Rotate, Ray, Intersect, etc. Suitable for middle school and above students learning geometric construction.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Point(Circle[B, a]) → C
  3. Segment(B, C) → b
  4. Angle(B, A, D_1) → α
  5. Rotate(B, α, C) → A'
  6. Ray(A, D_1) → c
  7. Ray(C, A') → d
  8. Intersect(c, d) → D
  9. Segment(A, D) → e
  10. Segment(C, D) → f
  11. Angle(B, C, D) → β
  12. Angle(C, D, A) → γ
  13. Angle(A, B, C) → δ
  14. Segment(A, C) → g
  15. Segment(B, D) → h
  16. Intersect(g, h) → E
  17. Angle(A, E, B) → ε
  18. Segment(A, E) → i
  19. Segment(C, E) → j
  20. Segment(B, E) → k
  21. Segment(D, E) → l
  22. Angle(A, B, E) → ζ
  23. Angle(C, B, E) → η
  24. Angle(C, D, E) → θ
  25. Angle(E, D, A) → ι
  26. Angle(B, C, E) → κ
  27. Angle(E, C, D) → λ
  28. Angle(D, A, E) → μ
  29. Angle(E, A, B) → ν