积极 AI Logo 积极 AI

等腰梯形的几何作图 by Julie Arakelian

等腰梯形的几何作图 by Julie Arakelian
几何画板及绘图内容加载中，请稍等……
2018-03-09 09:00
多边形解析几何变换几何作图
这个范例演示了等腰梯形的几何作图过程。核心数学概念包括梯形的性质、中点、斜率、垂直线、镜像、旋转等。通过使用GeoGebra命令如Line、Point、Midpoint、Slope、OrthogonalLine、Mirror、Rotate等，可以构造出等腰梯形。适合初中及以上学生学习几何作图和相关概念。

GeoGebra 命令及参数

  1. Line(A, B_1) → a
  2. Ray(A, B_1) → b
  3. Point(b) → B
  4. Midpoint(A, B) → D_1
  5. Line(A, B) → c
  6. Slope(c) → d
  7. OrthogonalLine(D_1, c) → g
  8. Point(g) → E_1
  9. Ray(D_1, E_1) → h
  10. Point(h) → F
  11. Slope(h) → i
  12. Line(F, c) → l
  13. Point(l) → G
  14. Point(l) → H
  15. Ray(F, G) → m
  16. Ray(F, H) → n
  17. Point(m) → D
  18. Mirror(D, h) → I'
  19. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], B) → A'
  20. Segment(A, A') → p
  21. Dilate(A, If[1 < o ≤ 2, 2 - o, 0], D) → A'_1
  22. Segment(A, A'_1) → q
  23. Segment(A, B) → r
  24. Segment(B, I') → s
  25. Segment(I', D) → t
  26. Segment(D, A) → a_1
  27. Circle(A, (0.2 * Min[a_1, r])) → c_1
  28. Circle(D, (0.2 * Min[a_1, r])) → d_1
  29. Intersect(d_1, a_1, 1) → J
  30. Intersect(d_1, t, 1) → K
  31. Intersect(c_1, r, 1) → L
  32. Intersect(c_1, a_1, 1) → M
  33. Dilate(D, If[2 < o ≤ 3, 3 - o, 0], I') → C
  34. Segment(D, C) → b_1
  35. Dilate(A, If[3 < o ≤ 4, 4 - o, 0], B) → A'_2
  36. Vector(A, A'_2) → u
  37. Translate(A, u) → A'_3
  38. Translate(A'_1, u) → N
  39. Segment(A'_3, N) → q'
  40. OrthogonalLine(A, r) → g_1
  41. Point(g_1) → O
  42. Angle(D, A, O) → α
  43. Angle(I', B, A) → β
  44. Rotate(A'_3, If[4 < o ≤ 5, (((o - 4) * 2) * α), (2 * α)], B) → P
  45. Rotate(N, If[4 < o ≤ 5, (((o - 4) * 2) * α), (2 * α)], B) → C_1
  46. Dilate(A, If[5 < o ≤ 6, 6 - o, 0], B) → A'_4
  47. Vector(A, A'_4) → v
  48. Dilate(D, If[7 < o ≤ 8, 8 - o, 0], I') → I'_2
  49. Vector(D, I'_2) → w
  50. Dilate(A, If[9 < o ≤ 10, 10 - o, 0], I') → A'_5
  51. Segment(A, A'_5) → i_1
  52. Dilate(A, If[10 < o ≤ 11, 11 - o, 0], D) → A'_6
  53. Vector(A, A'_6) → u_1
  54. Translate(A, u_1) → A'_7
  55. Translate(A'_5, u_1) → Q
  56. Segment(A'_7, Q) → j_1
  57. Segment(D, B) → l_1
  58. Angle(L, A, I') → γ
  59. Rotate(A'_7, If[11 < o ≤ 12, ((-(o - 11)) * (2 * γ)), (-2 * γ)], D) → R
  60. Rotate(Q, If[11 < o ≤ 12, ((-(o - 11)) * (2 * γ)), (-2 * γ)], D) → Q'
  61. Segment(R, Q') → m_1
  62. Polygon(A, B, I', D) → poly1, a_2, c_2, i', i_2
  63. Intersect(i_1, m_1) → E
  64. Distance(A, E) → distanceAS
  65. Distance(E, C_1) → distanceSN'
  66. Distance(E, B) → distanceSC
  67. Distance(E, D) → distanceSI
  68. Segment(B, I') → q''