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梯形与风筝形性质探索 by Charles Criniere

梯形与风筝形性质探索 by Charles Criniere
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2019-04-16 19:16
多边形角几何作图
①本范例演示等腰梯形与风筝形的几何性质；②涉及核心概念包括平行线、对角线、角平分线、对称性等；③作图要点：使用Segment（线段）、Rotate（旋转）、Angle（角度）、Point（点）、Line（直线）、Intersect（交点）等GeoGebra命令；④适合初中及以上学生用于探索几何图形性质，加深对相关定理的理解。

GeoGebra 命令及参数

  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