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Rotations of a Quadrilateral

Rotations of a Quadrilateral
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2015-10-06 19:35
PolygonAngleTrigonometryTransformationGeometric Construction
In collections Basic Rectangle Rotations
This example demonstrates the geometric transformation of rotating a quadrilateral around a point. It involves core concepts like rotation, angle, polygon construction, vector operations, and trigonometric functions. Key GeoGebra commands used include Polygon, Circle, Rotate, Angle, and Segment to construct and rotate the quadrilateral's vertices. Suitable for high school mathematics teaching to understand 2D transformations and applications in coordinate geometry.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D, E) → poly1, a, b, c, d, e
  2. Circle(O, D) → f
  3. Circle(O, C) → g
  4. Circle(O, A) → h
  5. Circle(O, E) → k
  6. Circle(O, B) → p
  7. Rotate(D, -Clockwise, O) → D'
  8. Angle(D', O, D) → β
  9. Rotate(C, -Clockwise, O) → C'
  10. Angle(C', O, C) → γ
  11. Rotate(B, -Clockwise, O) → B'
  12. Angle(B', O, B) → δ
  13. Rotate(A, -Clockwise, O) → A'
  14. Angle(A', O, A) → ε
  15. Rotate(E, -Clockwise, O) → E'
  16. Angle(E', O, E) → ζ
  17. Polygon(A', B', C', D', E') → poly2, a', b', c', d'_1, e'
  18. Rotate(D, Counterclockwise, O) → D''
  19. Angle(D, O, D'') → η
  20. Rotate(C, Counterclockwise, O) → C''
  21. Angle(C, O, C'') → θ
  22. Rotate(B, Counterclockwise, O) → B''
  23. Angle(B, O, B'') → ι
  24. Rotate(A, Counterclockwise, O) → A''
  25. Angle(A, O, A'') → κ
  26. Rotate(E, Counterclockwise, O) → E''
  27. Angle(E, O, E'') → λ
  28. Polygon(A'', B'', C'', D'', E'') → poly3, a'_1, b'_1, c'_1, d'_2, e'_1
  29. Segment(D, O) → l
  30. Segment(D', O) → m
  31. Angle(D', O, D) → α
  32. Segment(B, O) → n
  33. Segment(B', O) → q
  34. Angle(B', O, B) → μ
  35. Segment(A, O) → r
  36. Segment(A', O) → s
  37. Angle(A', O, A) → ν
  38. Segment(C, O) → a_1
  39. Segment(C', O) → b_1
  40. Angle(C', O, C) → ξ
  41. Angle(D, O, D'') → ρ
  42. Segment(D'', O) → e_1
  43. Segment(O, D) → f_1