MathPlotAI Logo MathPlotAI

Parallelogram Pyramid

Parallelogram Pyramid
Loading the math board and drawing, please wait…
2020-03-16 16:46
PolygonVectorCoordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the construction and properties of a parallelogram pyramid. It involves core mathematical concepts such as polygons, solid geometry, vectors, and coordinate geometry. Key GeoGebra commands used include Polygon, Pyramid, Net, OrthogonalLine, Intersect, Angle, PointIn, and Segment for building the geometric figure and auxiliary lines. Suitable for high school solid geometry teaching and learning, helping students understand the composition and calculation of spatial figures.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → q1, a, b, c, d
  2. Pyramid(q1, f) → g, F, faceABF, faceBCF, faceCDF, faceADF, edgeAF, edgeBF, edgeCF, edgeDF
  3. Net(g, OpenClose) → h, E, faceEGJ, faceGHK, faceHIL, faceEIM, edgeEG, edgeGH, edgeHI, edgeEI, edgeEJ, edgeGJ, G, edgeGK, edgeHK, edgeHL, edgeIL, edgeIM, edgeEM, H, I, J, K, L, M, faceEGHI
  4. OrthogonalLine(B, edgeEI, space) → i
  5. Intersect(i, edgeEI) → N
  6. Angle(B, N, A) → α
  7. PointIn(faceEGHI) → PointfaceEGHI
  8. OrthogonalLine(K, edgeGH, space) → k
  9. Intersect(k, edgeGH) → O
  10. Angle(K, O, B) → β
  11. OrthogonalLine(M, edgeEI, space) → m
  12. Intersect(m, edgeEI) → P
  13. Angle(M, P, D) → γ
  14. OrthogonalLine(J, edgeEG, space) → p
  15. OrthogonalLine(L, edgeHI, space) → q
  16. Intersect(edgeHI, q) → Q
  17. Angle(L, Q, C) → δ
  18. Intersect(edgeEG, p) → S
  19. Angle(J, S, A) → ζ
  20. Segment(S, J) → f_1
  21. Segment(P, M) → g_1
  22. Segment(Q, L) → h_1
  23. Segment(N, B) → i_1
  24. Segment(O, K) → j_1
  25. Segment(B, A) → k_1
  26. Segment(A, D) → l_1
  27. Segment(D, C) → m_1
  28. Segment(C, B) → n_1