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Similarity Transformations Exploration: Scaling and Length Study

Similarity Transformations Exploration: Scaling and Length Study
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2018-02-15 07:05
PolygonTransformationGeometric Construction
This example demonstrates the effects of scaling a figure under a central similarity transformation by changing the center and scale factor, observing the changes in the figure. Core mathematical concepts include similarity transformation, central symmetry, segment length ratio, and angle invariance. Construction highlights involve using GeoGebra commands like Polygon to draw polygons, Dilate for similarity transformations, Ray to create rays, Textfield for text annotations, Distance to measure lengths, Angle to measure angles, and Midpoint to find midpoints. It is suitable for high school mathematics students and teachers for learning and teaching demonstrations, aiding in understanding transformation geometry and proportional relationships.

GeoGebra Commands & Parameters

  1. Polygon(B, C, A) → poly1, d, b, c
  2. Dilate(B, a, O) → B'
  3. Dilate(C, a, O) → C'
  4. Dilate(A, a, O) → A'
  5. Polygon(B', C', A') → poly1', d', b', c'
  6. Ray(O, B') → e
  7. Ray(O, A') → f
  8. Ray(O, C') → g
  9. Textfield(a) → inputBox1
  10. Distance(O, C') → distanceOF
  11. Distance(C', C) → distanceFC
  12. Distance(B, C) → distanceBC
  13. Distance(B', C') → distanceEF
  14. Distance(A', C') → DF
  15. Distance(A, C) → AC
  16. Distance(C', B') → FE
  17. Distance(C, B) → CB
  18. Angle(C', B', A') → α
  19. Angle(C, B, A) → β
  20. Angle(A', C', B') → γ
  21. Angle(A, C, B) → δ
  22. Distance(O, B) → distanceOB
  23. Midpoint(O, B) →
  24. Distance(B, B') → distanceBB'
  25. Midpoint(B, B') →
  26. Distance(O, A) → distanceOA
  27. Midpoint(O, A) →
  28. Distance(O, A') → distanceOA'
  29. Midpoint(O, A') →
  30. Distance(O, C) → distanceOC
  31. Midpoint(O, C) →
  32. Distance(O, C') → distanceOC'
  33. Midpoint(O, C') →
  34. Distance(O, B') → distanceOB'
  35. Midpoint(O, B') →