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AAA Exploration in Hyperbolic Geometry

AAA Exploration in Hyperbolic Geometry
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2020-02-24 22:01
TriangleAngleTrigonometryGeometric ConstructionSlider Animation
This example demonstrates whether triangles with equal angles are congruent in hyperbolic geometry. Key math concepts include hyperbolic geometry, triangle congruence criteria, angle measurement, and distance calculation. Constructed using GeoGebra commands like Textfield, AngleofGivenSize, Point, HAngleMeasure, HDistance. Suitable for high school and above students to explore the differences between hyperbolic and Euclidean geometry and understand non-Euclidean geometric properties.

GeoGebra Commands & Parameters

  1. Textfield(a) → InputBox2
  2. Textfield(b) → InputBox3
  3. Textfield(c) → InputBox1
  4. AngleofGivenSize(D, A, a) → d, e
  5. Point(d) → B
  6. AngleofGivenSize(A, B, (-b)) → g, h
  7. Point(h) → C
  8. AngleofGivenSize(B, C, (-c)) → k, p
  9. HAngleMeasure(C, B, A) → α
  10. Point(p) → E
  11. HAngleMeasure(B, C, E) → β
  12. Point(e) → F
  13. HAngleMeasure(B, A, F) → γ
  14. HDistance(A, B) → i, text2
  15. HDistance(B, C) → j, text3
  16. HDistance(A, C) → l, text5