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Dilations and Trigonometric Ratios

Dilations and Trigonometric Ratios
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2016-06-16 22:11
TrigonometryTransformationGeometric Construction
This example demonstrates the geometric properties and relationship between trigonometric ratios under similarity transformations. Core math concepts include similarity transformation, trigonometric ratios, and angle measurement. GeoGebra commands and objects used in construction are Segment, OrthogonalLine, Rotate, Line, Intersect, Angle, Circle, CircleArc, Dilate, Polygon. Suitable for high school mathematics teaching to understand the connection between transformations and trigonometric functions.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. OrthogonalLine(B, f) → g
  3. Rotate(B, 45°, A) → B'
  4. Line(A, B') → h
  5. Intersect(g, h) → C
  6. Segment(B, C) → i
  7. Segment(C, A) → j
  8. Angle(C, B, A) → α
  9. Circle(A, C) → c
  10. Intersect(c, k, 2) → D
  11. CircleArc(A, D, C) → d
  12. Segment(A, D) → l
  13. Dilate(C, a, A) → C'
  14. Dilate(B, a, A) → B'_1
  15. Dilate(D, a, A) → D'
  16. Dilate(d, a, A) → d'
  17. Dilate(A, a, A) → A'
  18. Dilate(D, a, A) → D'_1
  19. Segment(A', D'_1) → l'
  20. Dilate(C, a, A) → C'_1
  21. Dilate(A, a, A) → A'_1
  22. Segment(C'_1, A'_1) → j'
  23. Dilate(B, a, A) → B'_2
  24. Dilate(C, a, A) → C'_2
  25. Segment(B'_2, C'_2) → i'
  26. Dilate(A, a, A) → A'_2
  27. Dilate(B, a, A) → B'_3
  28. Segment(A'_2, B'_3) → f'
  29. Angle(C', B'_1, A) → β
  30. Polygon(A, B, C) → poly1, c_1, a_1, b
  31. Angle(B, A, C) → γ