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Properties of a Kite by Alfred Estberg

Properties of a Kite by Alfred Estberg
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2014-11-12 00:59
PolygonTrigonometryGeometric Construction
This example demonstrates the geometric properties of a kite, involving core math concepts like polygons, isosceles triangles, and trigonometric functions. It uses commands such as Segment, Mirror, Polygon, OrthogonalLine, Intersect, Point, Circle, Rotate, and Midpoint in GeoGebra for construction. Suitable for middle school and above students to learn polygon properties and geometric constructions.

GeoGebra Commands & Parameters

  1. Segment(A, C) → a
  2. Mirror(B, a) → D
  3. Polygon(A, B, C, D) → poly1, a_1, b_1, c, d
  4. OrthogonalLine(D, a_1) → f_1
  5. Intersect(f_1, a_1) → Q
  6. Point(Segment[Q, B]) → K
  7. Circle(A, ((2 * ReflectPerp) * Segment[A, K])) → s
  8. OrthogonalLine(K, a_1) → r
  9. Intersect(r, c) → R
  10. Mirror(A, r) → A'_2
  11. Intersect(s, Line[A, A'_2]) → M, N
  12. Mirror(D, r) → D'_1
  13. Circle(D, (ReflectPerp * Segment[D, D'_1])) → t
  14. Intersect(t, Line[D, D'_1]) → O, P
  15. Segment(B, D) → b
  16. Intersect(a, b) → E
  17. Circle(B, (Distance[B, D] * ReflectAC / 10)) → e
  18. Intersect(e, b) → F, J
  19. Polygon(A, F, C) → poly2, f, p, q
  20. Mirror(C, Line[B, D]) → C'
  21. Mirror(A, Line[B, D]) → A'
  22. Circle(C, (Distance[C, C'] * ReflectBD / 10)) → g
  23. Intersect(g, Line[A, C], 1) → G
  24. Circle(A, (Distance[A, A'] * ReflectBD / 10)) → h
  25. Intersect(h, Segment[A, A']) → H, I
  26. Polygon(B, H, D, G) → poly3, k, l, m, n
  27. Rotate(A, α, E) → A'_1
  28. Rotate(B, α, E) → B'
  29. Rotate(C, α, E) → C'_1
  30. Rotate(D, α, E) → D'
  31. Polygon(A'_1, B', C'_1, D') → poly1', a'_1, b', c'_1, d'
  32. Segment(A'_1, C'_1) → i
  33. Segment(B', D') → j
  34. Midpoint(D, D'_1) → L
  35. Polygon(R, K, N, P) → q1, g_1, h_1, c_1, d_1
  36. Polygon(A, J, C) → t1, c_2, a_2, j_2