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Reflection Triangle and Collinear Points

Reflection Triangle and Collinear Points
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2015-02-17 21:01
TriangleCircle
In collections A Tour of Triangle Geometry
This example demonstrates the triangle A'B'C' formed by reflecting the vertices of triangle ABC in the opposite sides, and explores the relationship between the original triangle and the reflected triangle. Key mathematical concepts include reflection transformation, properties of circles, and triangle properties. It is constructed using GeoGebra commands such as Line, Polygon, Circle, Mirror, etc. Suitable for high school geometry learning and exploring the properties of reflection transformations.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Line(B, C) → b
  3. Line(C, A) → c
  4. Polygon(A, B, C) → poly1, c_1, a_1, b_1
  5. Circle(A, B, C) → s
  6. Mirror(A, b) → A'
  7. Mirror(B, c) → B'
  8. Mirror(C, a) → C'
  9. Line(C', B') → d
  10. Line(B', A') → e
  11. Line(A', C') → f
  12. Polygon(C', B', A') → poly2, a', c', b'
  13. Circle(C', B', A') → g
  14. Center(g) → O'
  15. Center(s) → O
  16. Midpoint(B, C) → D
  17. Midpoint(C, A) → E
  18. Midpoint(A, B) → F
  19. OrthogonalLine(A, b) → i
  20. OrthogonalLine(C, a) → j
  21. Circle(A, C', B') → h
  22. Circle(C, B', A') → k
  23. Circle(B, C', A') → p
  24. Intersect(h, k, 2) → G
  25. Line(O, O') → l

AI Drawing Prompt Reference

Draw triangle ABC and reflect its vertices A, B, C across the opposite sides b, c, a to get A', B', C'. Connect C'B', B'A', A'C' to form reflected triangle C'B'A'. Draw circles centered at ABC and C'B'A', label their centers as O and O', and draw a line between O and O'. Finally, draw three circles centered at A, C', B', C, B', A', and B, C', A', and find the intersection point of the first two circles.
The prompt above was compiled from the original drawing commands and is for reference only.