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Medians and Inequalities

Medians and Inequalities
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2016-03-28 02:07
TriangleInequalityGeometric Construction
This example demonstrates the relationship between medians and inequalities in triangles. Core concepts include median lines, inequalities, and triangle properties. Construction involves commands like Segment, Point, Distance, Semicircle, OrthogonalLine, Intersect, Center, Tangent, Angle, Polygon. Suitable for high school mathematics education to understand the median theorem and inequality applications.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a_1
  2. Point(a_1) → C
  3. Distance(C, B) → distanceCB
  4. Distance(A, C) → distanceAC
  5. Segment(D, E) → b_1
  6. Semicircle(D, E) → c
  7. Point(b_1) → F
  8. Segment(D, F) → a
  9. Segment(F, E) → b
  10. OrthogonalLine(F, b) → f
  11. Intersect(c, f, 1) → K
  12. Segment(F, K) → g
  13. Center(c) → L
  14. Segment(F, K) → h
  15. OrthogonalLine(L, b) → j
  16. Intersect(c, j, 1) → N
  17. Tangent(K, c) → l,
  18. Point(l) → T
  19. Point(l) → U
  20. Segment(T, U) → m
  21. OrthogonalLine(F, m) → n_1
  22. Angle(j, b) → α
  23. Angle(K, F, E) → β
  24. Intersect(n_1, m) → V
  25. Polygon(F, K, V) → poly1, v, f_1, k_1
  26. Angle(poly1) → γ, δ, ε
  27. Segment(F, N) → p
  28. Segment(L, N) → q
  29. Segment(F, V) → r
  30. Segment(D, K) → d
  31. Segment(K, E) → e
  32. Segment(W, Z) → i