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Similar Triangles (side lengths)

Similar Triangles (side lengths)
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2016-03-02 02:08
TriangleGeometric Construction
This example demonstrates the properties and criteria of similar triangles, dynamically showing the proportional relationships between corresponding side lengths. Key math concepts include similarity criteria, side ratios, and angle equality. Construction involves commands like Segment, Rotate, Angle, Line, Intersect, Polygon, and Distance, highlighting geometric construction techniques. Suitable for high school geometry instruction to enhance understanding and application of similar triangles.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Rotate(B, α, A) → B'
  3. Angle(B, A, B') → β
  4. Rotate(A, (-γ), B) → A'
  5. Angle(A', B, A) → δ
  6. Line(A', B) → b
  7. Line(A, B') → c
  8. Intersect(b, c) → C
  9. Polygon(C, A, B) → poly1, b_1, c_1, a_1
  10. Segment(D, F) → a_3
  11. Rotate(F, α, D) → B'_1
  12. Angle(F, D, B'_1) → β_1
  13. Rotate(D, (-γ), F) → A'_1
  14. Angle(A'_1, F, D) → δ_1
  15. Line(A'_1, F) → b_3
  16. Line(D, B'_1) → c_3
  17. Intersect(b_3, c_3) → E
  18. Polygon(E, D, F) → poly1_1, b_2, c_2, a_2
  19. Angle(E, F, D) → ε
  20. Angle(F, D, E) → ζ
  21. Distance(A, C) → distanceAC
  22. Distance(C, B) → distanceCB
  23. Distance(B, A) → distanceBA
  24. Distance(E, D) → distanceED
  25. Distance(D, F) → distanceDF
  26. Distance(F, E) → distanceFE