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Exploring Sections of a Triangular Prism

Exploring Sections of a Triangular Prism
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2019-06-29 06:57
TrigonometrySolid GeometryGeometric Construction
This example demonstrates how to investigate different cross-sections of a triangular prism by intersecting it with various planes. It involves core mathematical concepts such as solid geometry, cross-section geometry, and geometric transformations. The construction utilizes commands like Polygon, PointIn, Translate, Rotate, Prism, Plane, IntersectPath, and OrthogonalLine. Suitable for high school geometry instruction or student exploration of geometric cross-sections.

GeoGebra Commands & Parameters

  1. Polygon(B + (-2, -2), B + (2, -2), B + (2, 2), B + (-2, 2)) → poly3, e, f, g, i
  2. PointIn(poly3) → C
  3. Translate((0, 0, 0), Vector[B, C]) → A
  4. Polygon(A + (-4, -4), A + (4, -4), A + (4, 4), A + (-4, 4)) → poly1, a, b, c, d
  5. Rotate(Rotate[Translate[poly1, Vector[A, A + (0, 0, h)]], (90° * s), A + (0, 0, h), yAxis], (90° * t), A, zAxis) → poly2
  6. Rotate(D, 120°, (0, 0, 0)) → E
  7. Polygon(D, E, 3, xOyPlane) → poly4, j, k, l, F
  8. Prism(poly4, D + (0, 0, 4)) → m, M, edge4, edge5, edge6, N, face1, face2, face3, face4, edge1, edge2, edge3
  9. PointIn(poly2) → G
  10. PointIn(poly2) → H
  11. PointIn(poly2) → I
  12. Plane(G, I, H) → n
  13. IntersectPath(n, m) → poly6, poly5, r, a_1, b_1, c_1, K, L_1, O, P, J, L, p, q
  14. Rotate(m, 0, zAxis) → m'
  15. Rotate(m, 0, zAxis) → m'_1
  16. OrthogonalLine(A, n) → d_1