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Midpoint Parallelograms

Midpoint Parallelograms
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2015-12-04 17:55
PolygonComplex NumberInequalityGeometric Construction
This example demonstrates constructing a parallelogram using the midpoints of a quadrilateral's vertices. It involves core mathematical concepts like parallelograms, complex numbers, orthocenter, step functions, inequalities, and parabolas. The construction uses commands such as Polygon and Midpoint in GeoGebra. Suitable for high school mathematics education or geometric construction learning.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → poly1, a_{12}, b_{11}, c_{12}, d_{12}
  2. Midpoint(a_{12}) → E
  3. Midpoint(d_{12}) → F
  4. Midpoint(c_{12}) → G
  5. Midpoint(b_{11}) → H
  6. Polygon(A_1, B_1, C_1, D_1) → poly1_1, a_7, b_{10}, c_7, d_7
  7. Midpoint(a_7) → E_1
  8. Midpoint(d_7) → F_1
  9. Midpoint(c_7) → G_1
  10. Midpoint(b_{10}) → H_1
  11. Polygon(A_2, B_2, C_2, D_2) → poly1_2, a_8, b_7, c_8, d_8
  12. Midpoint(a_8) → E_2
  13. Midpoint(d_8) → F_2
  14. Midpoint(c_8) → G_2
  15. Midpoint(b_7) → H_2
  16. Polygon(A_3, B_3, C_3, D_3) → poly1_3, a_9, b_8, c_9, d_9
  17. Midpoint(a_9) → E_3
  18. Midpoint(d_9) → F_3
  19. Midpoint(c_9) → G_3
  20. Midpoint(b_8) → H_3
  21. Polygon(A_4, B_4, C_4, D_4) → poly1_4, a_{10}, b_9, c_{10}, d_{10}
  22. Midpoint(a_{10}) → E_4
  23. Midpoint(d_{10}) → F_4
  24. Midpoint(c_{10}) → G_4
  25. Midpoint(b_9) → H_4
  26. Polygon(A_5, B_5, C_5, D_5) → poly1_5, a_{11}, c, c_{11}, d_{11}
  27. Midpoint(a_{11}) → E_5
  28. Midpoint(d_{11}) → F_5
  29. Midpoint(c_{11}) → G_5
  30. Midpoint(c) → H_5
  31. Polygon(F, G, H, E) → poly2, a_6, b_6, c_6, d_6
  32. Polygon(F_1, G_1, H_1, E_1) → poly2_1, a_5, b_5, c_5, d_5
  33. Polygon(F_2, G_2, H_2, E_2) → poly2_2, b_2, c_2, d_2, a_2
  34. Polygon(F_3, G_3, H_3, E_3) → poly2_3, b_3, c_3, d_3, a_3
  35. Polygon(F_4, G_4, H_4, E_4) → poly2_4, a_4, b_4, c_4, d_4
  36. Polygon(F_5, G_5, H_5, E_5) → poly2_5, b_1, c_1, d_1, a_1