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Parallellogram Dimensions Demo

Parallellogram Dimensions Demo
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2018-02-26 17:46
PolygonVectorGeometric Construction
In collections Folding paper, doing geometry figures
This example demonstrates the geometric construction and dimensional relationships of a parallelogram. It involves core mathematical concepts such as polygon construction, midpoints, circular arcs, line segments, rotations, intersections, orthogonal lines, and angles. The construction utilizes commands and objects like Polygon, Midpoint, CircleArc, Segment, Rotate, Intersect, OrthogonalLine, Line, Point, and Angle in GeoGebra. It is suitable for high school mathematics education, helping students understand the properties and construction methods of parallelograms.

GeoGebra Commands & Parameters

  1. Polygon(A, C, D, B) → vierhoek1, a, c, d, b
  2. Midpoint(B, D) → BD
  3. Midpoint(A, C) → F
  4. Midpoint(B, E) → G
  5. CircleArc(B, DD, D) → e
  6. Segment(B, E) → f
  7. Polygon(B, A, C, E) → vierhoek2, b_1, a_1, c_1, e_1
  8. Polygon(B, E, D) → driehoek1, d_1, b_2, e_2
  9. Rotate(B, (((-(s - 1)) * 180))°, e_1) → B'
  10. Rotate(E, (((-(s - 1)) * 180))°, e_1) → E'
  11. Rotate(D, (((-(s - 1)) * 180))°, e_1) → D'
  12. Polygon(B', E', D') → driehoek1', d', b', e'
  13. Polygon(DD, E, B) → driehoek2, b_3, dd, e_3
  14. Segment(G, F) → g
  15. Polygon(G, F, C, E) → vierhoek3, g_1, f_1, c_2, e_4
  16. Polygon(B, A, F, G) → vierhoek4, b_4, a_2, f_2, g_2
  17. Rotate(G, (((-(s - 3)) * 180))°, f_2) → G'
  18. Rotate(F, (((-(s - 3)) * 180))°, f_2) → F'
  19. Rotate(C, (((-(s - 3)) * 180))°, f_2) → C'
  20. Rotate(E, (((-(s - 3)) * 180))°, f_2) → E'_1
  21. Polygon(G', F', C', E'_1) → vierhoek3', g', f', c', e'_1
  22. Polygon(A, F, G, DD) → vierhoek5, a_3, f_3, g_3, dd_1
  23. Segment(FE, F) → i
  24. Polygon(FE, A, F) → driehoek3, f_4, fe, a_4
  25. Rotate(FE, (((-(s - 5)) * 180))°, i) → FE'
  26. Rotate(A, (((-(s - 5)) * 180))°, i) → A'
  27. Rotate(F, (((-(s - 5)) * 180))°, i) → F'_1
  28. Polygon(FE', A', F'_1) → driehoek3', f'_1, fe', a'
  29. Polygon(B, FE, F, G) → vierhoek6, b_5, fe_1, f_5, g_4
  30. Intersect(g_3, i) → H
  31. OrthogonalLine(H, g', xOyPlane) → j
  32. Line(BD, F) → n
  33. Point(n) → K
  34. CircleArc(K, C, A) → p
  35. Polygon(G, H, F) → driehoek4, f_6, g_5, h_1
  36. Intersect(f_6, Line[FE, GG]) → J
  37. OrthogonalLine(H, b) → k
  38. Intersect(f_5, k) → I
  39. Polygon(G, H, I) → driehoek5, i_1, g_6, h_2
  40. Polygon(FE, F, L) → driehoek6, l, fe_2, f_7
  41. Intersect(f_6, f_7) → M
  42. Segment(G, M) → m
  43. Segment(H, M) → q
  44. Segment(B, D) → r
  45. Angle(A, B, E) → α
  46. Angle(G, F, FE) → β
  47. Segment(D, C) → t
  48. Segment(A, C) → j_1
  49. Segment(A, FE) → k_1
  50. Segment(G, BD) → l_1
  51. Segment(G, BD) → m_1
  52. Segment(G, E) → n_1
  53. CircleArc(F, FA, A) → h

AI Drawing Prompt Reference

Draw a parallelogram with points A, B, C, D, and E. First, draw quadrilateral ABCD. Then, find the midpoints F and G of BD and AC, respectively. Next, draw triangles BDE and BEC. Use rotation to generate new triangles and quadrilaterals. Finally, draw the diagonals of the parallelogram and related angles and line segments.
The prompt above was compiled from the original drawing commands and is for reference only.