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Midpoint Construction by JM Arranz, JA Mora, M Sada y R Losada

Midpoint Construction by JM Arranz, JA Mora, M Sada y R Losada
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2023-03-19 18:23
PolygonCoordinate GeometryGeometric Construction
In collections geometriadinamica.es
This example demonstrates how to construct polygons using midpoints. Key mathematical concepts include midpoints, segments, and polygons. It uses commands like Polygon, Midpoint, and Segment in GeoGebra. Suitable for middle school and above students learning geometric construction.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → poly1, a, b, c, d
  2. Midpoint(d) → E
  3. Midpoint(c) → F
  4. Midpoint(b) → G
  5. Midpoint(a) → H
  6. Polygon(E, F, G, H) → poly2, e, f, g, h
  7. Segment(A, C) → i
  8. Midpoint(i) → I
  9. Polygon(D, E, F) → poly3, f_1, d_1, e_1
  10. Polygon(E, I, F) → poly4, f_2, e_2, i_1
  11. Polygon(H, G, B) → poly5, b_1, h_1, g_1
  12. Polygon(H, I, G) → poly6, g_2, h_2, i_2
  13. Polygon(E, H, I) → poly7, i_3, e_3, h_3
  14. Polygon(F, G, C) → poly8, c_1, f_3, g_3
  15. Polygon(E, A, H) → poly9, h_4, e_4, a_1
  16. Polygon(F, I, G) → poly10, g_4, f_4, i_4

AI Drawing Prompt Reference

Draw a polygon defined by four points, then find the midpoint of each side to form a smaller polygon inside. Connect the diagonals of the original polygon and locate their midpoints. Finally, create several smaller polygons using these midpoints and the vertices of both the original and inner polygons to illustrate the midpoint construction process.
The prompt above was compiled from the original drawing commands and is for reference only.