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Perimeters and Areas of Similar Polygons by L Sliver

Perimeters and Areas of Similar Polygons by L Sliver
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2018-05-15 01:52
PolygonTrigonometryGeometric Construction
This example demonstrates the relationship between perimeters and areas of similar polygons. Key math concepts include the ratio of perimeters equals the similarity ratio, and the ratio of areas equals the square of the similarity ratio. It is constructed using GeoGebra commands like Circle, Rotate, Segment, Radius, Point, Angle, Polygon, Area, and Perimeter. Suitable for high school mathematics education to understand geometric properties of similar figures.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Rotate(B, 33, A) → B'
  3. Rotate(B', 2, A) → B''
  4. Rotate(B'', 1, A) → B'''
  5. Segment(B, B') → a
  6. Segment(B', B'') → b
  7. Segment(B'', B''') → d
  8. Segment(B''', B) → e
  9. Radius(c) → g
  10. Circle(C, (f * g)) → h
  11. Point(h) → D
  12. Rotate(D, 33, C) → D'
  13. Rotate(D', 2, C) → D''
  14. Rotate(D'', 1, C) → D'''
  15. Segment(D, D') → i
  16. Segment(D', D'') → j
  17. Segment(D'', D''') → k
  18. Segment(D''', D) → l
  19. Angle(B'', B', B) → α
  20. Angle(B, B''', B'') → β
  21. Angle(B''', B'', B') → γ
  22. Angle(B', B, B''') → δ
  23. Angle(D'', D', D) → ε
  24. Angle(D', D, D''') → ζ
  25. Angle(D, D''', D'') → η
  26. Angle(D''', D'', D') → θ
  27. Polygon(B', B, B''', B'') → poly1, b', b_1, b''', b''
  28. Polygon(D', D, D''', D'') → poly2, d', d_1, d''', d''
  29. Area(poly1) → Area_1
  30. Area(poly2) → Area_2
  31. Perimeter(poly1) → Perimeter_1
  32. Perimeter(poly2) → Perimeter_2

AI Drawing Prompt Reference

Draw two similar quadrilaterals, one formed by points B, B', B'', B''' and the other by points D, D', D'', D'''. Rotate point B to get B', then B'' and B''', and connect these points to form the first quadrilateral. Rotate point D to get D', then D'' and D''', and connect these points to form the second quadrilateral. Measure and calculate the perimeters and areas of the two quadrilaterals.
The prompt above was compiled from the original drawing commands and is for reference only.