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相似三角形构造

相似三角形构造
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2016-12-13 06:26
测试改名0函数几何作图
这个范例演示了如何构造相似三角形。核心数学概念包括相似三角形的性质。使用了Segment, PointIn, If, Union等GeoGebra命令。适合初中及以上学生学习相似三角形的几何作图。

GeoGebra 命令及参数

  1. Segment(A, B) → a
  2. Segment(B, C) → b
  3. Segment(C, A) → c
  4. PointIn(Polygon[(0.5, 0), (24, 0), (24, 13), (0.5, 13)]) → A'
  5. PointIn(Polygon[(0.5, 0), (24, 0), (24, 13), (0.5, 12)]) → C'
  6. PointIn(Polygon[(0.5, 0), (24, 0), (24, 13), (0.5, 12)]) → B'
  7. Segment(A', B') → d
  8. Segment(B', C') → e
  9. Segment(C', A') → f
  10. If(Distance[A, B] / Distance[A', B'] ≟ Distance[B, C] / Distance[B', C'] ∧ Distance[A, B] / Distance[A', B'] ≟ Distance[A, C] / Distance[A', C'] ∨ Distance[A, B] / Distance[A', B'] ≟ Distance[B, C] / Distance[A', C'] ∧ Distance[A, B] / Distance[A', B'] ≟ Distance[A, C] / Distance[B', C'] ∨ Distance[A, B] / Distance[A', C'] ≟ Distance[B, C] / Distance[C', B'] ∧ Distance[A, B] / Distance[A', C'] ≟ Distance[A, C] / Distance[A', B'] ∨ Distance[A, B] / Distance[A', C'] ≟ Distance[B, C] / Distance[B', A'] ∧ Distance[A, B] / Distance[A', C'] ≟ Distance[A, C] / Distance[B', C'] ∨ Distance[A, B] / Distance[B', C'] ≟ Distance[B, C] / Distance[B', A'] ∧ Distance[A, B] / Distance[B', C'] ≟ Distance[A, C] / Distance[A', C'] ∨ Distance[A, B] / Distance[B', C'] ≟ Distance[B, C] / Distance[A', C'] ∧ Distance[A, B] / Distance[B', C'] ≟ Distance[A, C] / Distance[A', B'], true, false) → similar
  11. Union(Sequence[Segment[(0, i), (25, i)], i, 0, 12], Sequence[Segment[(k, 0), (k, 12)], k, 0, 25]) → grid
  12. If(similar ∧ Polygon[A, B, C] ≟ Polygon[A', B', C'], true, false) → congruent