MathPlotAI Logo MathPlotAI

Three Triangles with Areas in Geometric Progression

Three Triangles with Areas in Geometric Progression
Loading the math board and drawing, please wait…
2016-02-17 21:02
TriangleSequenceGeometric Construction
In collections Besondere Punkte/Special Points
This example demonstrates three triangles with areas in geometric progression. It involves the concept of geometric sequences, adjusting the side lengths to change their areas. The construction uses commands like Polygon, OrthogonalLine, Intersect, Segment, and Angle. Suitable for high school mathematics, particularly in geometry and sequence-related courses.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → Tr, c, a, b
  2. OrthogonalLine(A, a) → d
  3. OrthogonalLine(B, b) → e
  4. OrthogonalLine(C, c) → f
  5. Intersect(d, e) → H
  6. Intersect(d, a) → A'
  7. Intersect(e, b) → B'
  8. Intersect(f, c) → C'
  9. Polygon(A', B', C') → Tr', c', a', b'
  10. OrthogonalLine(A, a') → g
  11. OrthogonalLine(B, b') → h
  12. OrthogonalLine(C, c') → i
  13. Intersect(g, a') → A''
  14. Intersect(h, b') → B''
  15. Intersect(i, c') → C''
  16. Segment(A, A'') → j
  17. Segment(B, B'') → k
  18. Segment(C, C'') → l
  19. Polygon(A'', B'', C'') → Tr'', c'', a'', b''
  20. Angle(A, A'', C') → α_1
  21. Angle(B, B'', A') → β_1
  22. Angle(C, C'', B') → γ_1
  23. Segment(A, A') → m
  24. Segment(B, B') → n
  25. Segment(C, C') → p
  26. Angle(C', A, B') → α
  27. Angle(C, A', B') → α''
  28. Angle(C', A', B) → α'
  29. Angle(C, B, A) → β
  30. Angle(A, B', C') → β''
  31. Angle(A', B', C) → β'
  32. Angle(B', C, A') → γ
  33. Angle(B, C', A') → γ''
  34. Angle(B', C', A) → γ'