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Properties of Non Isosceles and Isosceles Trapezoids

Properties of Non Isosceles and Isosceles Trapezoids
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2018-03-16 07:15
PolygonAngleGeometric Construction
This example illustrates the properties of non-isosceles and isosceles trapezoids. Key mathematical concepts include the definition and properties of trapezoids, as well as the special properties of isosceles trapezoids. Construction highlights the use of Segment, OrthogonalLine, Point, Intersect, Angle, Line, LineBisector, Mirror, and Midpoint commands in GeoGebra. Suitable for middle and high school students learning about trapezoids.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. OrthogonalLine(A, f) → g
  3. OrthogonalLine(B, f) → h
  4. Point(g) → C
  5. OrthogonalLine(C, g) → i
  6. Intersect(h, i) → D
  7. Segment(C, D) → j
  8. Point(j) → E
  9. Point(j) → F
  10. Segment(E, F) → k
  11. Segment(A, E) → l
  12. Segment(B, F) → m
  13. Angle(A, E, F) → α
  14. Angle(E, F, B) → β
  15. Angle(F, B, A) → γ
  16. Angle(B, A, E) → δ
  17. Segment(G, H) → n
  18. Line(I, n) → p
  19. LineBisector(n) → q
  20. Mirror(I, q) → J
  21. Segment(G, I) → r
  22. Segment(I, J) → s
  23. Segment(J, H) → t
  24. Angle(H, G, I) → ε
  25. Angle(G, I, J) → ζ
  26. Angle(I, J, H) → η
  27. Angle(J, H, G) → θ
  28. Segment(I, H) → GJ
  29. Segment(J, G) → IH
  30. Segment(K, L) → a
  31. Line(M, a) → b
  32. Point(b) → N
  33. Segment(M, N) → c
  34. Segment(K, M) → d
  35. Segment(N, L) → e
  36. Midpoint(d) → O
  37. Midpoint(e) → P
  38. Segment(O, P) → f_1