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利用变换判断两个三角形是否相似 by Mark Hampton

利用变换判断两个三角形是否相似 by Mark Hampton
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2015-01-17 03:06
测试改名0变换几何作图
所属专题 Geometry - Transformations for similarity and congruence Geometry - Transformations for similarity and congruence
本范例演示如何利用变换判断两个三角形是否相似。核心数学概念涉及相似三角形的性质和变换。通过使用GeoGebra命令如If, Circle, Point, Line, Intersect, Polygon, OrthogonalLine, Segment, Dilate, Angle, Vector等，可以构造出两个三角形并进行变换操作。适合初中及以上学生学习相似三角形的相关知识。

GeoGebra 命令及参数

  1. If(b < c, (b * 0.25), (c * 0.25)) → HandleRadius
  2. Circle(A, HandleRadius) → d
  3. Point(d) → Rotate
  4. Line(Rotate, A) → e
  5. Circle(A, b) → f
  6. Intersect(f, e, 2) → B
  7. Circle(B, a) → g
  8. Circle(A, c) → h
  9. Intersect(g, h, 2) → C
  10. Intersect(g, h, 1) → C'
  11. Polygon(A, B, C) → poly1, c_1, a_1, b_1
  12. OrthogonalLine(A, e) → i
  13. If(b < c, (b * 0.5), (c * 0.5)) → FlipHandleRadius
  14. Circle(A, FlipHandleRadius) → k
  15. Intersect(k, i) → E, F
  16. Segment(F, E) → j
  17. Point(j) → Reflect
  18. Polygon(A, B, C') → poly2, d_1, a_2, b_2
  19. Segment(Reflect, C) → l
  20. Segment(Reflect, C') → m
  21. Segment(A, Reflect) → n
  22. Segment(A, Rotate) → p
  23. Polygon(M, P, T) → poly3, p_1, m_1, n_1
  24. Dilate(A, dilation, A) → A'
  25. Dilate(B, dilation, A) → B'
  26. Dilate(C', dilation, A) → C''
  27. Polygon(A', B', C'') → poly2', c'', a', b'
  28. Dilate(A, dilation, A) → A'_1
  29. Dilate(B, dilation, A) → B'_1
  30. Dilate(C, dilation, A) → C'''
  31. Polygon(A'_1, B'_1, C''') → poly1', c'_1, a'_1, b'_1
  32. Circle(A, 0.2) → q
  33. Intersect(d, r, 1) → D
  34. Angle(Rotate, A, D) → α
  35. Vector(AStartValue, A) → u