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Taxicab Geometry Counterexamples for Congruent Triangles

Taxicab Geometry Counterexamples for Congruent Triangles
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2020-02-18 23:20
TriangleCoordinate GeometryGeometric Construction
This example demonstrates counterexamples of congruent triangles in taxicab geometry. It involves key mathematical concepts such as triangle congruence, taxicab geometry distance, and angle measurement. Using GeoGebra commands like Segment, ProperAngleMeasure, and TDist, specific conditions are met to construct triangles that are not congruent. Suitable for high school geometry and math enthusiasts.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(B, C) → g
  3. Segment(C, A) → h
  4. Segment(A', C') → i
  5. Segment(C', B') → j
  6. Segment(B', A') → k
  7. ProperAngleMeasure(A', C', B') → α, text1
  8. ProperAngleMeasure(A', B', C') → β, text2
  9. ProperAngleMeasure(B', A', C') → γ, text3
  10. ProperAngleMeasure(A, B, C) → δ, text4
  11. ProperAngleMeasure(B, A, C) → ε, text5
  12. ProperAngleMeasure(A, C, B) → ζ, text6
  13. TDist(A, B) → text7, a
  14. TDist(B, C) → text8, b
  15. TDist(C, A) → text9, c
  16. TDist(A', B') → text10, d
  17. TDist(B', C') → text11, e
  18. TDist(C', A') → text12, l
  19. Segment(D, E) → n
  20. Segment(E, F) → p
  21. Segment(F, D) → q
  22. Segment(F', E') → r
  23. Segment(E', D') → s
  24. Segment(D', F') → t
  25. ProperAngleMeasure(D, E, F) → η, text13
  26. ProperAngleMeasure(D, F, E) → θ, text14
  27. ProperAngleMeasure(E, D, F) → ι, text15
  28. ProperAngleMeasure(E', D', F') → κ, text16
  29. ProperAngleMeasure(D', E', F') → λ, text17
  30. ProperAngleMeasure(E', F', D') → μ, text18
  31. TDist(D, E) → text19, o
  32. TDist(E, F) → text20, u
  33. TDist(F, D) → text21, v
  34. TDist(D', E') → text22, w
  35. TDist(E', F') → text23, a_1
  36. TDist(F', D') → text24, b_1

AI Drawing Prompt Reference

Draw two triangles ABC and A'B'C', where the taxicab distances of AB, BC, and CA are a, b, and c respectively, and the taxicab distances of A'B', B'C', and C'A' are d, e, and l respectively. Ensure that the corresponding angles of triangles ABC and A'B'C' are not equal, and the side lengths of triangle ABC are a, b, and c, while the side lengths of triangle A'B'C' are d, e, and l, but triangles ABC and A'B'C' are not congruent.
The prompt above was compiled from the original drawing commands and is for reference only.