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Vecten Problem: Geometric Exploration with Squares and Triangles

Vecten Problem: Geometric Exploration with Squares and Triangles
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2015-08-05 00:23
TrianglePolygonAngleTrigonometryGeometric Construction
① This GeoGebra example demonstrates the Vecten configuration, where squares are constructed on the sides of a triangle, and explores the area relationships among the resulting shapes, with a full solution attached. ② Core mathematical concepts include triangle area, sine rule, square properties, trigonometry, and 2D vectors, with extensions to prisms and conic sections. ③ Construction highlights: using GeoGebra's Polygon command to create triangle poly1 and squares poly2 through poly7 on each side, Angle command to mark key angles, and points A, B, C with derived points D, E, F, G, H, I to build auxiliary lines; the command list includes polygons, angles, and side lengths. ④ Suitable for GCSE/IGCSE extension or high school geometry, this example trains students in area calculation, trigonometric identities, and integrated geometric construction.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Polygon(A, B, 4) → poly2, d, e, f, g, D, E
  3. Polygon(B, C, 4) → poly3, h, i, j, k, F, G
  4. Polygon(C, A, 4) → poly4, l, m, n_1, p, H, I
  5. Polygon(D, G, B) → poly5, b_1, d_1, g_1
  6. Polygon(E, A, H) → poly6, h_1, e_1, a_1
  7. Polygon(I, C, F) → poly7, f_1, i_1, c_1
  8. Angle(A, B, C) → α
  9. Angle(B, C, A) → β
  10. Angle(C, A, B) → γ
  11. Angle(E, A, H) → δ
  12. Angle(B, A, E) → ε
  13. Angle(D, B, A) → ζ
  14. Angle(A, E, D) → η
  15. Angle(E, D, B) → θ
  16. Angle(C, B, G) → ι
  17. Angle(G, F, C) → κ
  18. Angle(F, C, B) → λ
  19. Angle(B, G, F) → μ
  20. Angle(H, A, C) → ν
  21. Angle(A, C, I) → ξ
  22. Angle(C, I, H) → ο
  23. Angle(I, H, A) → ρ
  24. Angle(I, C, F) → σ
  25. Angle(G, B, D) → τ