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Angles on Rays

Angles on Rays
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2014-02-22 20:26
AngleTransformationGeometric Construction
This example demonstrates angles on rays. Key mathematical concepts include angle measurement and rotation. Using GeoGebra commands such as Intersect, Point, Rotate, Ray, etc., a series of angles can be constructed. Suitable for middle school and above students to learn geometry and trigonometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Point(xAxis) → V
  3. Rotate(V, (-α), O) → V'
  4. Ray(O, V) → a
  5. Ray(O, V') → b
  6. Point(a) → A
  7. Circle(O, A) → c
  8. Circle(A, O) → d
  9. Intersect(d, b) → B', B
  10. Circle(B, A) → e
  11. Intersect(e, a) → C', C
  12. Circle(C, B) → f
  13. Intersect(f, b) → D', D
  14. Circle(D, C) → g
  15. Intersect(g, a) → E', E
  16. Circle(E, D) → h
  17. Intersect(h, b) → F', F
  18. Circle(F, E) → k
  19. Intersect(k, a) → G', G
  20. Circle(G, F) → p
  21. Intersect(p, b) → H', H
  22. Circle(H, G) → q
  23. Intersect(q, a) → I', I
  24. Circle(I, H) → r
  25. Intersect(r, b) → J', J
  26. Segment(J, I) → i
  27. Segment(I, H) → j
  28. Segment(H, G) → l
  29. Segment(G, F) → m
  30. Segment(F, E) → n
  31. Segment(E, D) → s
  32. Segment(D, C) → t
  33. Segment(C, B) → a_1
  34. Segment(A, B) → b_1
  35. Angle(E, F, D) → β
  36. Angle(B, O, A) → γ

AI Drawing Prompt Reference

Draw two intersecting rays, then rotate one ray around the intersection point to form a series of intersecting circles and arcs. Start by taking point O on the x-axis as the rotation center, then take point V on the x-axis as the endpoint of the initial ray. Rotate V to get V', and draw two rays a and b starting from O and V' respectively. Then draw circles c, d, etc., using intersection points to form a series of arcs, and finally connect the endpoints of these arcs to form a polygon. Measure angles β and γ.
The prompt above was compiled from the original drawing commands and is for reference only.