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Compound Transformations between Two Triangles

Compound Transformations between Two Triangles
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2020-02-25 05:37
TriangleTransformationGeometric Construction
This example demonstrates compound transformations between two triangles, including dilation/contraction, translation, rotation, and reflection. It involves core mathematical concepts such as geometric transformations, vectors, polygons, and properties of triangles. Construction highlights the use of GeoGebra commands and objects like Polygon, Centroid, Dilate, Vector, Translate, Rotate, Mirror. Suitable for high school mathematics teaching and learning geometric transformations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → t1, c, a, b
  2. Centroid(t1) → D
  3. Dilate(A, d, D) → A'
  4. Dilate(B, d, D) → B'
  5. Dilate(C, d, D) → C'
  6. Polygon(A', B', C') → t1', c', a', b'
  7. InteriorAngles(t1) → t1A, t1B, t1C
  8. InteriorAngles(t1') → t1'A, t1'B, t1'C
  9. Vector(E, F) → u
  10. Translate(A', u) → A''
  11. Translate(B', u) → B''
  12. Translate(C', u) → C''
  13. Polygon(A'', B'', C'') → t1'', c'', a'', b''
  14. InteriorAngles(t1'') → t1''A, t1''B, t1''C
  15. Rotate(A'', α, A'') → A'''
  16. Rotate(B'', α, A'') → B'''
  17. Rotate(C'', α, A'') → C'''
  18. Polygon(A''', B''', C''') → t1''', c''', a''', b'''
  19. InteriorAngles(t1''') → t1'''A, t1'''B, t1'''C
  20. Mirror(A''', b''') → G
  21. Mirror(B''', b''') → H
  22. Mirror(C''', b''') → I
  23. Polygon(G, H, I) → t2, i, g, h
  24. InteriorAngles(t2) → t2A, t2B, t2C