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全等与相似三角形命名

全等与相似三角形命名
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2016-07-07 09:00
测试改名0角几何作图
①本范例演示如何通过 GeoGebra 动态演示全等与相似三角形的命名方法；②涉及核心数学概念包括全等三角形的 SSS, SAS, ASA, AAS 性质及相似三角形的 AA, SAS, SSS 性质；③作图要点运用了 Sequence, RandomElement, Rotate, Line, Intersect, Circle, If, Max, Polygon, Min, Shuffle, Angle, Take, Append 等命令及对象，实现三角形的随机生成与变换；④适合初中及以上数学教学，用于几何作图与定理验证教学。

GeoGebra 命令及参数

  1. Sequence(30° + ((i * 10))°, i, 0, 12) → listAlpha
  2. RandomElement(listAlpha) → α
  3. Sequence(((i * 10))°, i, 1, (180 - α / °) / 10 - 1) → listBeta
  4. RandomElement(listBeta) → β
  5. RandomElement({0.75, 1, 1.25}) → k
  6. Rotate(A, β, O) → A'
  7. Line(O, A') → LineOA'
  8. Rotate(O, (-α), A) → O'
  9. Line(A, O') → LineAO'
  10. Intersect(LineOA', LineAO') → B
  11. Circle(O'', (Distance[O, B] * k)) → c
  12. Rotate(Dilate[Translate[A, Vector[O, O'']], k, O''], If[rotate, theta, 0°], O'') → A''
  13. Circle(A'', (Distance[A, B] * k)) → d
  14. Intersect(c, d, 1) → B''1
  15. Intersect(c, d, 2) → B''2
  16. If(reflect, B''1, B''2) → B''
  17. Max({Distance[A, B], Distance[A, O], Distance[O, B]}) → maxLength
  18. Max({x(O), x(A), x(B), x(O''), x(A''), x(B'')}) → maxX
  19. Polygon(O, A, B) → poly1, b_1, c_1, a_1
  20. Min({x(O), x(A), x(B), x(O''), x(A''), x(B'')}) → minX
  21. Min({y(O), y(A), y(B), y(O''), y(A''), y(B'')}) → minY
  22. Max({y(O), y(A), y(B), y(O''), y(A''), y(B'')}) → maxY
  23. Shuffle({"D", "E", "F", "G", "H", "J", "K", "L", "M", "N", "P", "Q", "R", "S", "T", "V", "W", "X", "Y"}) → listLetter
  24. Angle(poly1) → angleO, angleA, angleB
  25. Polygon(B'', O'', A'') → poly2, a_2, b_2, c_2
  26. Angle(poly2) → angleB'', angleO'', angleA''
  27. Take(listLetter, 1, 3) → listQuestion
  28. Append("?", Take[listLetter, 4, 6]) → listAnswer1
  29. Append("?", Take[listLetter, 4, 6]) → listAnswer2
  30. Append("?", Take[listLetter, 4, 6]) → listAnswer3
  31. If(SelectedIndex[listAnswer1] ≟ 2, angleO'', If[SelectedIndex[listAnswer1] ≟ 3, angleA'', If[SelectedIndex[listAnswer1] ≟ 4, angleB'', 0°]]) → ans1
  32. If(SelectedIndex[listAnswer2] ≟ 2, angleO'', If[SelectedIndex[listAnswer2] ≟ 3, angleA'', If[SelectedIndex[listAnswer2] ≟ 4, angleB'', 0°]]) → ans2
  33. If(SelectedIndex[listAnswer3] ≟ 2, angleO'', If[SelectedIndex[listAnswer3] ≟ 3, angleA'', If[SelectedIndex[listAnswer3] ≟ 4, angleB'', 0°]]) → ans3