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Properties of an Isosceles Trapezoid by Alfred Estberg

Properties of an Isosceles Trapezoid by Alfred Estberg
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2014-11-12 01:06
PolygonAngleGeometric Construction
This example demonstrates the geometric properties and symmetry of an isosceles trapezoid. Key math concepts include polygons, symmetry axes, midlines, and angle relationships. Construction highlights involve commands like Segment, LineBisector, Mirror, Intersect, Circle, Polygon, Rotate, OrthogonalLine to draw and analyze the trapezoid's symmetry. Suitable for middle school and above students learning geometric constructions and property exploration.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Segment(D, A) → b
  3. LineBisector(a) → c
  4. Mirror(D, c) → C
  5. Segment(D, C) → d
  6. Segment(C, B) → e
  7. Segment(A, C) → f
  8. Segment(B, D) → g
  9. Intersect(f, g) → E
  10. Mirror(B, f) → B'
  11. Circle(B, (Distance[B, B'] * ReflectAC / 10)) → h
  12. Intersect(h, Segment[B, B']) → F, G
  13. Polygon(A, C, F) → poly1, j, l, m
  14. Mirror(A, g) → A'
  15. Circle(A, (Distance[A, A'] * ReflectBD / 10)) → k
  16. Intersect(k, Segment[A, A']) → I, J
  17. Polygon(D, B, J) → poly2, i, n, p
  18. Polygon(A, B, C, D) → poly3, a_1, b_1, c_1, d_1
  19. Rotate(A, α, E) → A'_1
  20. Rotate(B, α, E) → B'_1
  21. Rotate(C, α, E) → C'
  22. Rotate(D, α, E) → D'
  23. Polygon(A'_1, B'_1, C', D') → poly3', a'_1, b'_1, c', d'
  24. Segment(A'_1, C') → q
  25. Segment(B'_1, D') → r
  26. OrthogonalLine(D, d) → s
  27. OrthogonalLine(C, d) → t
  28. Intersect(s, a) → H
  29. Intersect(t, a) → K
  30. Segment(H, K) → f_1
  31. LineBisector(A, B) → g_1
  32. Intersect(g_1, d) → L
  33. Intersect(g_1, a) → M
  34. Circle(A, (ReflectPerp * Segment[A, B])) → e_1
  35. Circle(D, (ReflectPerp * Segment[C, D])) → h_1
  36. Intersect(h_1, d, 1) → N
  37. Intersect(e_1, a, 1) → O
  38. Polygon(L, N, O, M) → q1, l_2, n_2, o, m_2
  39. Intersect(h_1, d, 2) → P
  40. Polygon(P, L, M, O) → q2, p_2, l_3, m_3, o_2
  41. Polygon(D, B, I) → t1, i_2, d_2, b_2
  42. Polygon(A, C, G) → t2, g_2, a_2, c_2