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Similar Triangle Construction

Similar Triangle Construction
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2016-12-13 06:26
TriangleFunctionGeometric Construction
This example demonstrates the construction of similar triangles. Key mathematical concepts include the properties of similar triangles. It uses GeoGebra commands such as Segment, PointIn, If, and Union. Suitable for middle school and above students to learn about geometric construction of similar triangles.

GeoGebra Commands & Parameters

  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