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Pythagorean Inequality Activity

Pythagorean Inequality Activity
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2019-07-26 00:26
TriangleAngleInequalityGeometric ConstructionSlider Animation
This example demonstrates how students can classify triangles by their angles simply by knowing the lengths of their sides, involving key math concepts like Pythagorean Theorem, triangle classification, and inequalities. It uses commands like Line, Slope, Segment, Rotate, Angle, Ray, Point, Polygon, PointIn, Min, Max, Sort, Element in GeoGebra for geometric constructions and calculations, suitable for high school mathematics teaching to help students visually understand and discover the applications of Pythagorean Theorem and inequalities.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Slope(a) → m
  3. Segment(A, B) → d
  4. Rotate(B, α, A) → B'
  5. Angle(B, A, B') → β
  6. Ray(A, B') → e
  7. Point(e) → C
  8. Segment(A, B) → f
  9. Segment(B, C) → g
  10. Segment(A, C) → h
  11. Polygon(C, B, 4) → poly1, i, j, k, l, D, E
  12. Polygon(A, C, 4) → poly2, n, p, q, r, F, G
  13. Polygon(B, A, 4) → poly3, s, t, a_1, b_1, H, I
  14. PointIn(poly1) → Pointpoly1
  15. PointIn(poly2) → Pointpoly2
  16. PointIn(poly3) → Pointpoly3
  17. Polygon(A, B, C) → poly4, c_1, a_2, b_2
  18. Min(list) → o
  19. Max(list) → u
  20. Min(poly1, poly2) → v
  21. Min(poly2, poly3) → w
  22. Min(v, w) → d_1
  23. Sort(list) → list1
  24. Element(list1, 1) → poly5
  25. Element(list1, 2) → poly6
  26. Element(list1, 3) → poly7
  27. Angle(A, C, B) → γ
  28. Angle(C, B, A) → δ