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Tree Diagrams and Geometric Constructions

Tree Diagrams and Geometric Constructions
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2015-04-24 13:28
AngleCoordinate GeometryMatrixTransformationGeometric Construction
In collections Geometry of Angles (Student Created)
This example demonstrates how to use tree diagrams to illustrate geometric construction processes. Core math concepts include angles, segments, matrix transformations, and coordinate geometry. Construction highlights from the summary involve commands like Ray, Rotate, Angle, Segment, Line, Point, Intersect, and OrthogonalLine using GeoGebra. Suitable for high school and above learners to understand dynamic geometric constructions and transformations.

GeoGebra Commands & Parameters

  1. Ray(A, B) → a
  2. Rotate(C, -66*°, A) → C'
  3. Angle(C', A, C) → α
  4. Segment(A, C') → b
  5. Rotate(A, 106*°, C') → A'
  6. Angle(A, C', A') → β
  7. Segment(C', A') → c
  8. Line(A', a) → d
  9. Point(d) → D
  10. Rotate(C', -40*°, A') → C''
  11. Angle(C'', A', C') → γ
  12. Ray(A', D) → f
  13. Intersect(a, b) → E
  14. Point(a) → F
  15. Segment(E, F) → e
  16. Intersect(c, f) → G
  17. Point(f) → H
  18. Segment(G, H) → g
  19. Point(e) → I
  20. OrthogonalLine(I, e) → h
  21. Intersect(h, g) → J
  22. Rotate(A', -90*°, J) → A''
  23. Intersect(b, c) → K
  24. Rotate(A', 50*°, K) → A''_1
  25. Angle(A', K, A''_1) → ε
  26. Rotate(A, -24*°, K) → A'_1
  27. Angle(A'_1, K, A) → ζ
  28. OrthogonalLine(K, e) → i
  29. Intersect(i, e) → L
  30. Intersect(i, g) → M
  31. Segment(L, M) → j
  32. Rotate(A', -90*°, M) → A''_2
  33. Angle(A''_2, M, A') → δ
  34. Rotate(A, 90*°, L) → A'_2
  35. Angle(A, L, A'_2) → η
  36. Line(A', e) → l
  37. Point(l) → N
  38. Ray(A', N) → m
  39. Rotate(K, 140*°, A') → K'
  40. Angle(K, A', K') → θ
  41. Line(A, g) → n
  42. Point(n) → O
  43. Ray(A, O) → p
  44. Angle(O, A, K) → ι