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Similarity Test #3

Similarity Test #3
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2015-12-03 03:22
PolygonAngleTrigonometryGeometric ConstructionSlider Animation
This example demonstrates the determination and properties of polygon similarity; involves core math concepts like polygons, ratios, triangles, reflection, set theory, general quadrilateral, natural numbers, orthocenter; construction highlights the use of Rotate, Angle, Line, Point, Segment, Polygon, Circle, Intersect commands and objects in GeoGebra; suitable for high school mathematics teaching to explore properties and transformation rules of similar figures.

GeoGebra Commands & Parameters

  1. Rotate(A, α, B) → A'
  2. Angle(A, B, A') → β
  3. Line(A', B) → a
  4. Line(B, A) → b
  5. Point(a) → C
  6. Segment(B, C) → d
  7. Segment(B, A) → e
  8. Polygon(C, B, A) → poly1, a_1, c_1, b_1
  9. Point(Circle[D, abs(q)]) → E
  10. Segment(D, E) → c
  11. Rotate(E, α, D) → E'
  12. Angle(E, D, E') → γ
  13. Line(D, E') → f
  14. Point(Circle[D, abs(p)]) → F
  15. Segment(D, F) → g
  16. Circle(D, F) → h
  17. Intersect(h, f, 2) → G
  18. Polygon(G, D, E) → poly2, e_1, g_1, d_1
  19. Angle(B, C, A) → δ
  20. Angle(D, G, E) → ε
  21. Angle(G, E, D) → ζ
  22. Angle(C, A, B) → η

AI Drawing Prompt Reference

Draw a polygon demonstrating similarity through rotation and line connections, highlighting angle and side ratio relationships, involving triangles and circles, with a slider for rotation angles to explore geometric transformations and similarity proofs.
The prompt above was compiled from the original drawing commands and is for reference only.