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Rotation of a Triangle

Rotation of a Triangle
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2012-03-07 11:02
TriangleTransformation
This example demonstrates various properties of triangle rotation. Key mathematical concepts include geometric transformations, specifically rotation. Using GeoGebra commands such as Polygon, Rotate, and Segment, the construction of the rotated triangle is illustrated. Suitable for middle school and above students learning geometric transformations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Rotate(A, α, D) → A'
  3. Rotate(B, α, D) → B'
  4. Rotate(C, α, D) → C'
  5. Polygon(A', B', C') → poly1', c', a', b'
  6. Rotate(A, α, B) → A'_2
  7. Rotate(B, α, B) → B'_2
  8. Rotate(C, α, B) → C'_2
  9. Polygon(A'_2, B'_2, C'_2) → poly1'_1, c'_2, a'_2, b'_2
  10. Segment(B', D) → f
  11. Segment(C', D) → g
  12. Segment(A', D) → h
  13. Segment(C, D) → i
  14. Segment(B, D) → j
  15. Segment(A, D) → k
  16. Segment(A, B) → l
  17. Segment(C, B) → m
  18. Segment(C'_2, B) → n
  19. Segment(A'_2, B) → p
  20. Circle(D, A) → r
  21. Circle(D, B) → s
  22. Circle(D, C) → t
  23. Circle(B, A) → c_1
  24. Circle(B, C) → d_1
  25. Textfield(D) → inputBox1

AI Drawing Prompt Reference

Draw a triangle ABC, then rotate it twice around point D by angle α. First, rotate triangle ABC around point D to get triangle A'B'C', and then rotate it around point B to get triangle A'_2B'_2C'_2. Draw the sides of triangles A'B'C' and A'_2B'_2C'_2, including the segments from each vertex to point D, and the corresponding sides of triangles ABC and A'_2B'_2C'_2.
The prompt above was compiled from the original drawing commands and is for reference only.