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Trapezoids and the Harmonic Mean by Norm Prokup

Trapezoids and the Harmonic Mean by Norm Prokup
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2016-06-21 05:08
PolygonFunctionTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the geometric relationship between trapezoids and the harmonic mean. It involves core math concepts like trapezoid properties, harmonic mean definition, and coordinate geometry calculations. GeoGebra commands and objects used include Line, Point, Segment, Intersect, and Angle for construction. Suitable for high school mathematics education to understand the connection between special quadrilaterals and sequence averages.

GeoGebra Commands & Parameters

  1. Line(D, C) → f
  2. Line(A, f) → g
  3. Point(g) → B
  4. Line(D, A) → h
  5. Line(B, C) → i
  6. Segment(A, C) → j
  7. Segment(B, D) → k
  8. Segment(D, C) → b
  9. Segment(A, D) → m
  10. Segment(B, C) → n
  11. Segment(A, B) → a
  12. Intersect(j, k) → E
  13. Line(E, b) → q
  14. Intersect(h, q) → P
  15. Intersect(i, q) → Q
  16. Segment(P, Q) → r
  17. Segment(E, Q) → l
  18. Segment(P, E) → p
  19. Angle(C, D, A) → α
  20. Angle(E, P, A) → β
  21. Angle(A, E, P) → γ
  22. Angle(E, C, D) → δ
  23. Angle(B, Q, E) → ε
  24. Angle(Q, C, D) → ζ
  25. Angle(Q, E, B) → η
  26. Angle(C, D, E) → θ