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Trapezoid and Kite Property Exploration by Charles Criniere

Trapezoid and Kite Property Exploration by Charles Criniere
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2019-04-16 19:16
PolygonAngleGeometric Construction
This example demonstrates the geometric properties of isosceles trapezoids and kites, involving concepts like parallel lines, diagonals, angle bisectors, and symmetry. Constructed using commands such as Segment, Rotate, Angle, Point, Line, and Intersect in GeoGebra. Ideal for middle school and above to explore and understand related theorems.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Rotate(B, α, A) → B'
  3. Angle(B, A, B') → β
  4. Rotate(A, (-α), B) → A'
  5. Angle(A', B, A) → γ
  6. Segment(A, B') → b
  7. Segment(B, A') → c
  8. Point(b) → C
  9. Line(C, a) → d
  10. Intersect(c, d) → D
  11. Segment(A, C) → e
  12. Segment(C, D) → f
  13. Segment(D, B) → g
  14. Segment(B, C) → h
  15. Segment(A, D) → i
  16. Intersect(h, i) → E
  17. Segment(E, A) → j
  18. Segment(E, B) → k
  19. Segment(E, C) → l
  20. Segment(E, D) → m
  21. Angle(A, C, D) → δ
  22. Angle(C, D, B) → ε
  23. Angle(C, E, A) → ζ
  24. Angle(D, E, C) → η
  25. Angle(B, E, D) → θ
  26. Angle(A, E, B) → ι
  27. Rotate(G, κ, F) → G'
  28. Angle(G, F, G') → μ
  29. Rotate(G, (-λ), F) → G'_1
  30. Angle(G'_1, F, G) → ν
  31. Rotate(F, (-κ), G) → F'
  32. Angle(F', G, F) → ξ
  33. Rotate(F, λ, G) → F'_1
  34. Angle(F, G, F'_1) → ο
  35. Segment(F, G) → p
  36. Segment(F, G') → q
  37. Segment(G, F') → r
  38. Segment(F, G'_1) → s
  39. Segment(G, F'_1) → t
  40. Intersect(s, t) → H
  41. Intersect(q, r) → I
  42. Segment(H, I) → a_1
  43. Intersect(p, a_1) → J
  44. Segment(F, H) → b_1
  45. Segment(H, G) → c_1
  46. Segment(G, I) → d_1
  47. Segment(F, I) → e_1
  48. Segment(F, J) → f_1
  49. Segment(J, G) → g_1
  50. Segment(J, I) → h_1
  51. Segment(J, H) → i_1
  52. Angle(I, G, H) → ρ
  53. Angle(G, H, F) → σ
  54. Angle(F, I, G) → τ
  55. Angle(H, F, I) → υ
  56. Angle(F, J, H) → ϕ
  57. Angle(I, J, F) → χ
  58. Angle(G, J, I) → ψ
  59. Angle(H, J, G) → ω