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Isosceles Trapezoid Investigation Template

Isosceles Trapezoid Investigation Template
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2016-01-14 22:48
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This example demonstrates the geometric properties and construction of an isosceles trapezoid. It involves core math concepts like polygons, angles, geometric construction, and symmetry. Key GeoGebra commands used include Segment, Midpoint, OrthogonalLine, Intersect, Mirror, Angle, and Polygon for drawing and analyzing the trapezoid's features. Suitable for middle school and above students for geometric exploration and property discovery.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Midpoint(a) → C_1
  3. OrthogonalLine(C_1, a) → b
  4. Segment(A, D) → c
  5. OrthogonalLine(D, b) → d
  6. Intersect(b, d) → E
  7. Segment(D, E) → e
  8. Mirror(D, b) → C_2
  9. Mirror(E, b) → E'
  10. Segment(C_2, E') → e'
  11. Mirror(A, b) → B_2
  12. Mirror(D, b) → C
  13. Segment(B_2, C) → c'
  14. Segment(D, C_2) → f
  15. Segment(A, C_2) → g
  16. Segment(D, B) → h
  17. Intersect(g, h) → F
  18. Segment(A, F) → i
  19. Segment(F, C_2) → j
  20. Segment(D, F) → k
  21. Segment(F, B) → l
  22. Angle(D, C_2, F) → α
  23. Angle(F, C_2, B) → β
  24. Angle(A, D, F) → γ
  25. Angle(F, D, C_2) → δ
  26. Angle(B, A, F) → ε
  27. Angle(F, A, D) → ζ
  28. Angle(F, B, A) → η
  29. Angle(C_2, B, F) → θ
  30. Angle(B, A, D) → ι
  31. Angle(A, D, C_2) → κ
  32. Angle(D, C_2, B) → λ
  33. Angle(C_2, B, A) → μ
  34. Polygon(A, B, C) → poly1, c_1, a_1, b_1
  35. Mirror(A, i) → A'
  36. Mirror(B, i) → B'
  37. Mirror(C, i) → C'
  38. Polygon(A', B', C') → poly1', c'_1, a', b'
  39. Polygon(D, A, B) → poly2, b_2, d_1, a_2
  40. Mirror(D, l) → D'
  41. Mirror(A, l) → A'_1
  42. Mirror(B, l) → B'_1
  43. Polygon(D', A'_1, B'_1) → poly2', b'_1, d', a'_1