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Isosceles Trapezoid Lune

Isosceles Trapezoid Lune
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2015-06-19 01:13
TransformationGeometric ConstructionLocus
This example demonstrates the geometric construction of an isosceles trapezoid lune. Key mathematical concepts include similarity transformation, rectangle, parabola, hyperbola, and right triangles. Construction involves GeoGebra commands such as Segment, Circle, OrthogonalLine, Intersect, Midpoint, Line, Polygon, LineBisector, and CircleSector. Suitable for middle or high school mathematics education to understand geometric transformations and properties.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Circle(B, A) → c
  3. OrthogonalLine(B, a) → b
  4. Intersect(c, b) → C_1, D_1
  5. Segment(A, C_1) → d
  6. OrthogonalLine(A, d) → e
  7. Circle(A, B) → f
  8. Intersect(f, e) → E, F
  9. Segment(E, C_1) → g
  10. Circle(E, Segment[A, B]) → h
  11. Intersect(h, g) → G,
  12. Midpoint(G, C_1) → H
  13. Circle(B, Segment[H, C_1]) → k
  14. Circle(A, Segment[H, C_1]) → p
  15. Line(A, B) → i
  16. Intersect(p, i) → I, J
  17. Intersect(k, i) → K, L
  18. OrthogonalLine(I, i) → j
  19. OrthogonalLine(L, i) → l
  20. Circle(B, A) → q
  21. Intersect(q, l) → M, N
  22. Circle(A, B) → r
  23. Intersect(r, j) → C, P
  24. Polygon(A, B, M, C) → TRAPEZOID, a_1, b_1, m, o
  25. LineBisector(A, B) → n
  26. LineBisector(C, A) → s
  27. Intersect(s, n) → Q
  28. Circle(Q, B) → t
  29. CircleSector(Q, A, C) → sett_1
  30. CircleSector(Q, B, A) → sett_2
  31. CircleSector(Q, M, B) → sett_3
  32. Polygon(C, Q, A) → triang_1, a_2, o_1, q_1
  33. Polygon(Q, A, B) → triang_2, b_2, q_2, a_3
  34. Polygon(Q, B, M) → triang_3, m_1, q_3, b_3
  35. Line(M, a_3) → c_1
  36. Line(C, o_1) → d_1
  37. Intersect(c_1, d_1) → R
  38. Polygon(R, M, C) → TRIANG, o_2, r_1, m_2
  39. Intersect(o_2, r_1) → D
  40. CircleSector(R, D, C) → SETT

AI Drawing Prompt Reference

Please draw an isosceles trapezoid lune. The figure includes an isosceles trapezoid, three triangles, and several circular sectors. The construction order: first draw the isosceles trapezoid, then construct circles and lines, then construct triangles and sectors. Ensure the figure follows geometric transformations and properties.
The prompt above was compiled from the original drawing commands and is for reference only.