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Cross Sections of a Triangular Prism

Cross Sections of a Triangular Prism
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2016-05-10 19:03
PolygonSolid GeometryGeometric Construction
①This example dynamically cuts a triangular prism with a plane to visually explore how the cross-section shape changes with different positions and angles, helping students understand the relationship between planes and solids in 3D geometry. ②Core mathematical concepts include the structure of a triangular prism, cross-section polygons formed by plane-solid intersection, and applications of parallelism and perpendicularity in space. ③Construction highlights: the Prism command builds the triangular prism, a Plane and OrthogonalLine define the cutting plane, IntersectPath computes the intersection lines with each face, and Point, Polygon objects allow dynamic adjustment of the cutting position to generate the final cross-section. ④It is suitable for high school or early college students learning solid geometry, and for teachers to demonstrate in class to enhance spatial visualization and geometric intuition.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 3) → poly1, a, b, c, C
  4. Prism(poly1, 3.586878522587578) → d, D, edgeCF, edgeDE, edgeEF, edgeDF, E, F, faceABED, faceBCFE, faceACFD, faceDEF, edgeAD, edgeBE
  5. Point(edgeCF) → G
  6. OrthogonalLine(G, edgeBE, space) → e
  7. OrthogonalLine(G, edgeAD, space) → f
  8. Intersect(edgeBE, e) → H
  9. Intersect(edgeAD, f) → I
  10. Plane(H, G, I) → g
  11. IntersectPath(g, d) → poly2, J, K, L, h, i, j
  12. Point(edgeDE) → M
  13. Point(edgeDF) → N
  14. OrthogonalLine(M, a, space) → l
  15. Point(l) → O
  16. Plane(M, N, O) → m
  17. IntersectPath(m, d) → poly3, P, Q, R, S, n, p, q, r
  18. Point(edgeEF) → T
  19. Point(edgeDE) → U
  20. Point(edgeBE) → V
  21. Plane(U, T, V) → s
  22. IntersectPath(s, d) → poly4, W, Z, A_1, t, a_1, b_1
  23. Point(edgeBE) → B_1
  24. Point(edgeAD) → C_1
  25. Point(edgeCF) → D_1
  26. Plane(B_1, C_1, D_1) → v
  27. IntersectPath(v, d) → poly5, E_1, F_1, G_1, c_1, d_1, e_1

AI Drawing Prompt Reference

Draw a triangular prism and cut it with a plane to observe how the cross-section shape changes with different positions and angles. First, create a triangle using the Polygon command, then build the triangular prism with the Prism command. Define a cutting plane and compute the intersection lines with each face to generate the cross-section. Finally, dynamically adjust the cutting position to produce various cross-section shapes.
The prompt above was compiled from the original drawing commands and is for reference only.