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Similar Right Triangles and Trig Ratios

Similar Right Triangles and Trig Ratios
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2019-06-26 09:48
TriangleTrigonometryCoordinate Geometry
This example quickly creates right triangles by plotting two points and entering an acute angle measure. It demonstrates the properties of similar right triangles and trigonometric ratios. Commands used include Segment, OrthogonalLine, Textfield, Rotate, Angle, Ray, Intersect, Polygon. Suitable for middle school and above students learning trigonometry and geometric construction.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. OrthogonalLine(B, f) → g
  3. Textfield(α) → InputBox1
  4. Rotate(B, α, A) → B'
  5. Angle(B, A, B') → β
  6. Ray(A, B') → h
  7. Intersect(g, h) → C
  8. Polygon(A, B, C) → t1, c, a, b
  9. Segment(B, C) → i
  10. Segment(C, A) → j
  11. Angle(C, B, A) → γ
  12. Segment(D, E) → f_1
  13. OrthogonalLine(E, f_1) → g_1
  14. Textfield(α) → InputBox1_1
  15. Rotate(E, α, D) → B'_1
  16. Angle(E, D, B'_1) → β_1
  17. Ray(D, B'_1) → h_1
  18. Intersect(g_1, h_1) → F
  19. Polygon(D, E, F) → t1_1, c_1, a_1, b_1
  20. Segment(E, F) → i_1
  21. Segment(F, D) → j_1
  22. Angle(F, E, D) → γ_1
  23. Segment(D, E) → k
  24. Segment(E, F) → l
  25. Segment(F, D) → m
  26. Angle(E, D, F) → δ

AI Drawing Prompt Reference

Draw a right triangle quickly by plotting two points and entering an acute angle. Show the properties of similar right triangles and trigonometric ratios. Start with a line segment, then draw a perpendicular line from one endpoint. Input an acute angle, rotate the segment around the other endpoint to this angle to form a second right triangle. Label the three angles and three sides of both triangles and calculate trigonometric values.
The prompt above was compiled from the original drawing commands and is for reference only.