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Midpoint Triangles

Midpoint Triangles
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2015-11-09 15:12
TriangleFunctionCoordinate GeometryTransformationGeometric Construction
This example demonstrates constructing midpoint triangles from a given triangle by connecting midpoints of its sides, exploring properties like area relationships, medians, rotations, and connections to quadratic functions. It involves core concepts in coordinate geometry and transformation. The construction uses commands like Polygon, Midpoint, Rotate, and PointIn. Suitable for high school mathematics education to investigate geometric relationships and function graphs.

GeoGebra Commands & Parameters

  1. Polygon(A, K, L) → poly5, l, j, k
  2. Midpoint(l) → M
  3. Midpoint(j) → N
  4. Midpoint(k) → O
  5. Polygon(M, O, N) → poly6, n, m, o
  6. Polygon(A, M, O) → poly7, o_1, j_1, m_1
  7. Polygon(M, K, N) → poly8, n_1, m_2, k_1
  8. Polygon(O, N, L) → poly9, l_1, o_2, n_2
  9. Midpoint(n) → P
  10. Midpoint(o) → Q
  11. Midpoint(m) → R
  12. Rotate(A, Rotate, P) → J'
  13. Rotate(M, Rotate, P) → M'
  14. Rotate(O, Rotate, P) → O'
  15. Polygon(J', M', O') → poly7', o', j', m'
  16. Rotate(M, Rotate, Q) → M'_1
  17. Rotate(K, Rotate, Q) → K'
  18. Rotate(N, Rotate, Q) → N'
  19. Polygon(M'_1, K', N') → poly8', n', m'_1, k'
  20. Rotate(O, Rotate, R) → O'_1
  21. Rotate(N, Rotate, R) → N'_1
  22. Rotate(L, Rotate, R) → L'
  23. Polygon(O'_1, N'_1, L') → poly9', l', o'_1, n'_1
  24. PointIn(poly5) → Pointpoly5_1
  25. PointIn(poly5) → Pointpoly5_2
  26. PointIn(poly5) → Pointpoly5_3
  27. PointIn(poly5) → Pointpoly5