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Pythagorean Triples and Inequalities

Pythagorean Triples and Inequalities
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2016-09-20 21:29
TriangleInequalityGeometric Construction
This example demonstrates Pythagorean triples and related inequalities. By constructing a right triangle, it illustrates the application of the Pythagorean theorem. Using GeoGebra commands such as Circle, Point, Segment, etc., it dynamically shows the relationship between the sides of a right triangle and the inequalities. Suitable for students at the junior high school level and above to learn geometry and inequalities.

GeoGebra Commands & Parameters

  1. Circle(C, b) → c
  2. Point(Circle[C, a]) → B
  3. Segment(C, B) → f
  4. Rotate(B, (-θ), C) → B'
  5. Angle(B', C, B) → α
  6. Ray(C, B') → g
  7. Intersect(c, g) → A,
  8. Segment(A, B) → h
  9. Segment(C, A) → i
  10. Angle(B, A, C) → β
  11. Angle(C, B, A) → γ
  12. Distance(A, B) → distanceAB
  13. Distance(B, C) → distanceBC
  14. Distance(A, C) → distanceAC
  15. Polygon(C, B, 4) → Area1, j, k, l, m, D, E
  16. Polygon(A, C, 4) → Area2, n, p, q, r, F, G
  17. Polygon(B, A, 4) → Area3, s, t, d, e, H, I