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Isosceles Trapezoid Investigation by atreitman

Isosceles Trapezoid Investigation by atreitman
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2016-01-25 23:28
PolygonVectorOptimizationGeometric Construction
This example demonstrates the geometric properties and vector relationships of an isosceles trapezoid. It involves core math concepts like polygons, vectors, angles, distances, midpoints, and linear programming. The construction uses commands and objects such as segments, lines, points, angle bisectors, reflections, slopes, angles, distances, midpoints, and intersections. Suitable for high school mathematics teaching, exploring geometric transformations and optimization problems.

GeoGebra Commands & Parameters

  1. Segment(B, A) → a
  2. Line(C_1, a) → b
  3. Point(b) → D
  4. Segment(A, D) → c
  5. LineBisector(a) → d
  6. Mirror(A, d) → A'
  7. Mirror(D, d) → C
  8. Segment(A', C) → c'
  9. Segment(D, C) → e
  10. Slope(a) → m
  11. Slope(e) → m_1
  12. Slope(c) → m_2
  13. Slope(c') → m_3
  14. Angle(A, B, C) → α
  15. Angle(B, C, D) → β
  16. Angle(C, D, A) → γ
  17. Angle(D, A, B) → C_2
  18. Distance(A, B) → distanceAB
  19. Midpoint(A, B) →
  20. Distance(B, C) → distanceBC
  21. Midpoint(B, C) →
  22. Distance(C, D) → distanceCD
  23. Midpoint(C, D) →
  24. Distance(D, A) → distanceDA
  25. Midpoint(D, A) →
  26. Segment(A, C) → i
  27. Segment(B, D) → j
  28. Intersect(i, j) → E
  29. Distance(A, E) → distanceAE
  30. Midpoint(A, E) →
  31. Distance(E, B) → distanceEB
  32. Midpoint(E, B) →
  33. Distance(E, C) → distanceEC
  34. Midpoint(E, C) →
  35. Distance(E, D) → distanceED
  36. Midpoint(E, D) →
  37. Angle(B, E, A) → δ
  38. Angle(A, E, D) → ε
  39. Angle(D, E, C) → ζ
  40. Angle(C, E, B) → η
  41. Angle(B, C, E) → θ
  42. Angle(E, C, D) → ι
  43. Angle(C, D, E) → κ
  44. Angle(E, D, A) → λ
  45. Angle(D, A, E) → μ
  46. Angle(E, A, B) → ν
  47. Angle(A, B, E) → ξ
  48. Angle(E, B, C) → ο