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Trig Ratios of Similar Triangles

Trig Ratios of Similar Triangles
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2018-06-24 00:27
TriangleTrigonometryGeometric Construction
This example demonstrates the equality of trigonometric ratios (sine, cosine, tangent) in similar triangles. It involves core concepts like similar triangles, trigonometric ratios, and the relationship between central angles and chords in a circle. Construction uses commands such as Intersect, Point, Ray, Rotate, Angle, OrthogonalLine, Distance, Segment, and Polygon. Suitable for high school mathematics education to understand the application of trigonometric functions in geometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Ray(A, B) → f
  4. Rotate(B, α, A) → B'
  5. Angle(B, A, B') → β
  6. Ray(A, B') → g
  7. Point(g) → C
  8. Point(g) → D
  9. OrthogonalLine(C, f) → h
  10. OrthogonalLine(D, f) → i
  11. Intersect(h, f) → E
  12. Intersect(i, f) → F
  13. Angle(C, E, A) → γ
  14. Angle(D, F, A) → δ
  15. Distance(A, C) → distanceAC
  16. Distance(A, E) → distanceAE
  17. Distance(E, C) → distanceEC
  18. Distance(A, F) → distanceAF
  19. Distance(F, D) → distanceFD
  20. Distance(A, D) → distanceAD
  21. Segment(C, E) → j
  22. Segment(D, F) → k
  23. Distance(F, D) → FD
  24. Distance(A, D) → AD
  25. Polygon(E, C, A) → poly1, a_1, e, c_1
  26. Segment(A, D) → l
  27. Segment(A, F) → m
  28. Polygon(A, F, D) → poly2, d_1, a_2, f_1