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Area Trisection of Parallelogram DEFH

Area Trisection of Parallelogram DEFH
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2014-10-27 07:03
PolygonTrigonometryGeometric Construction
In collections Dissecting a Triangle Into Three Equal Areas
This example demonstrates constructing a parallelogram DEFH where DE is one-third of BC and EF is half the length of the median from vertex A. Key mathematical concepts include similar triangles, median properties, and proportions. GeoGebra commands used include Polygon, Midpoint, Dilate, Segment, Line, and Intersect. Suitable for middle school and above students learning geometric construction.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Midpoint(B, A) → D_1
  3. Midpoint(A, C) → E_1
  4. Dilate(B, 0.3333333333333333, C) → E
  5. Dilate(B, 0.6666666666666666, C) → D
  6. Segment(D_1, E_1) → H_1
  7. Midpoint(B, C) → F_1
  8. Segment(A, F_1) → e
  9. Line(D, e) → f
  10. Line(E, e) → g
  11. Intersect(g, H_1) → F
  12. Intersect(f, H_1) → H
  13. Polygon(D, E, F, H) → poly2, d, e_1, f_1, h
  14. Midpoint(f_1) → I
  15. Polygon(A, B, D, H, I) → poly3, a_1, b_1, d_1, h_1, i
  16. Polygon(A, I, F, E, C) → poly4, a_2, i_1, f_2, e_2, c_1
  17. PointIn(poly4) → Pointpoly4
  18. PointIn(poly3) → Pointpoly3
  19. PointIn(poly2) → Pointpoly2