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Determining Similarity of Shapes

Determining Similarity of Shapes
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2017-01-17 02:29
PolygonAngleTransformationGeometric Construction
In collections Obstar Dilation and Similarity Exploration
This example demonstrates how to determine if two polygons are similar through similarity transformations. Key math concepts include similarity criteria, geometric transformations (scaling, rotation, reflection), and relationships between angles and side lengths. Construction highlights involve using Polygon, Dilate, Line, Mirror, Angle, and Segment commands in GeoGebra. Suitable for high school students learning geometric similarity.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → poly1, a, b, c, d
  2. Dilate(A, 2, E) → A'
  3. Dilate(B, 2, E) → B'
  4. Dilate(C, 2, E) → C'
  5. Dilate(D, 2, E) → D'
  6. Polygon(A', B', C', D') → poly1', a', b', c', d'
  7. Line(F, G) → e
  8. Mirror(A', e) → A''
  9. Mirror(B', e) → B''
  10. Mirror(C', e) → C''
  11. Mirror(D', e) → D''
  12. Polygon(A'', B'', C'', D'') → poly1'', a'', b'', c'', d''
  13. Line(B, B'') → f
  14. Line(D'', D) → g
  15. Line(A'', A) → h
  16. Line(C'', C) → i
  17. Angle(C, B, A) → CBA
  18. Angle(D, C, B) → DCB
  19. Angle(A, D, C) → ADC
  20. Angle(B, A, D) → BAD
  21. Angle(D'', A'', B'') → D'A'B'
  22. Angle(A'', B'', C'') → A'B'C'
  23. Angle(C'', D'', A'') → C'D'A'
  24. Angle(B'', C'', D'') → B'C'D'
  25. Segment(D, C) → j
  26. Segment(C, B) → k
  27. Segment(B, A) → l
  28. Segment(A, D) → m
  29. Segment(A'', D'') → n
  30. Segment(D'', C'') → p
  31. Segment(C'', B'') → q
  32. Segment(B'', A'') → r