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Triangular Pyramid by GeoGebra Materials Team

Triangular Pyramid by GeoGebra Materials Team
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2012-05-03 19:42
TriangleTrigonometrySolid Geometry
In collections Area, Surface Area, Volume--Nets
This example demonstrates the geometric construction and properties of a triangular pyramid. It involves mathematical concepts such as solid geometry, trigonometry, and vectors. The construction uses GeoGebra commands like Line, Circle, Intersect, Vector, etc. to create the base and apex of the pyramid. It is suitable for high school students or college students learning geometric construction and spatial visualization.

GeoGebra Commands & Parameters

  1. Line(J, K) → h
  2. Circle(J, base_1) → g
  3. Intersect(g, h, 1) → M
  4. Vector(J, M) → w
  5. Dilate(I, base, H) → L
  6. Vector(H, L) → v
  7. Translate(A, v) → B
  8. Midpoint(A, B) → C
  9. Midpoint(C, A) → D
  10. Translate(D, Vector[w / 2]) → N
  11. AngularBisector(A, N, B) → l
  12. AngularBisector(B, A, N) → k
  13. Intersect(k, l) → O
  14. Dilate(F, height, E) → G
  15. Vector(E, G) → u
  16. Translate(O, u) → D_1
  17. Circle(J, 1) → d
  18. Polygon(A, N, B) → P, b, a, n
  19. Polygon(D_1, A, N) → Q, n_1, n', a_1
  20. Polygon(D_1, B, N) → R, n_2, n'_1, b_1
  21. Polygon(A, D_1, B) → S, b_2, a_2, n'_2
  22. Segment(N, D) → c
  23. Midpoint(N, D) → T
  24. If(VolumeFormula ≟ 1, U) → Z
  25. If(VolumeSolution ≟ 1, V) → A_1
  26. Segment(D_1, O) → m
  27. Midpoint(D_1, O) → C_1

AI Drawing Prompt Reference

Draw a triangular pyramid with a base triangle and an apex, construct the sides by connecting the apex to the midpoints of the base triangle, and highlight the height and angle bisectors to illustrate its geometric properties.
The prompt above was compiled from the original drawing commands and is for reference only.