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Triangle, Trapezoid, Octagon Construction

Triangle, Trapezoid, Octagon Construction
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2017-02-17 19:54
PolygonVectorCoordinate Geometry
This example demonstrates the geometric construction and properties of triangles, trapezoids, and octagons. Key math concepts include polygons, vectors, geometric transformations, and coordinate geometry. Construction highlights the use of GeoGebra commands such as Intersect, Point, Polygon, Mirror, Segment, Midpoint, If, Vector, and Translate. Suitable for high school mathematics teaching or for geometry enthusiasts studying polygon construction and transformations.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 8) → poly1, f, D, E, F, G, H, g, h, i, j, k, l, m, C
  4. Polygon(A, E, B) → poly2, b, a, e
  5. Mirror(E, a) → E'
  6. Mirror(B, a) → B'
  7. Mirror(C, a) → C'
  8. Segment(C', B) → n
  9. Midpoint(C', A) → I
  10. Segment(I, B) → p
  11. If(0 < c < 1, Dilate[B, 1 - c, C], Dilate[B, 0, C]) → B'_1
  12. Vector(B, B'_1) → u
  13. Polygon(I, B, C') → poly3, c', i_1, b_1
  14. Translate(I, u) → I'
  15. Translate(B, u) → B'_2
  16. Translate(C', u) → C''
  17. Polygon(I', B'_2, C'') → poly3', c'', i', b'_2
  18. If(1 ≤ c < 2, Polygon[Rotate[I', (((-π)) / 4 * (c - 1)), C], Rotate[B'_2, (((-π)) / 4 * (c - 1)), C], Rotate[C'', (((-π)) / 4 * (c - 1)), C]], Polygon[Rotate[I', ((-π)) / 4, C], Rotate[B'_2, ((-π)) / 4, C], Rotate[C'', ((-π)) / 4, C]]) → poly4
  19. Polygon(A, I, B) → poly5, b_2, a_1, i_2
  20. If(3 ≤ c < 4, Dilate[B, 4 - c, E], Dilate[B, 0, E]) → K
  21. Vector(B, K) → v
  22. Translate(A, v) → A'
  23. Translate(I, v) → I'_1
  24. Translate(B, v) → B'_3
  25. Polygon(A', I'_1, B'_3) → poly5', b'_3, a', i'_1
  26. If(3 ≤ c < 4, Polygon[Rotate[A', ((3 * π / 4) * (c - 3)), K], Rotate[I'_1, ((3 * π / 4) * (c - 3)), K], Rotate[B'_3, ((3 * π / 4) * (c - 3)), K]], Polygon[Rotate[A', (3 * π / 4), K], Rotate[I'_1, (3 * π / 4), K], Rotate[B'_3, (3 * π / 4), K]]) → poly6
  27. Polygon(E, C', B) → poly7, b_3, e_1, c'_1
  28. If(c ≥ 5, Dilate[C', 6 - c, C], Dilate[C', 0, C]) → J
  29. Polygon(E, J, B) → poly8, b_4, e_2, j_1
  30. Polygon(E, A, B) → poly9, b_5, e_3, a_2