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Pyramid Section by a Parallel Plane

Pyramid Section by a Parallel Plane
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2015-06-17 22:28
Solid GeometryTransformationGeometric Construction
This example demonstrates the section of a pyramid by a plane parallel to its base. Key mathematical concepts include the properties of sections in solid geometry. Using GeoGebra commands such as Translate, IntersectPath, and OrthogonalLine, various faces of the pyramid and the section can be constructed. Suitable for high school geometry education or students learning solid geometry.

GeoGebra Commands & Parameters

  1. Translate(xOyPlane, Vector[(108.97273250105863, -56.3843553230339, 60)]) → b
  2. Pyramid(A, B, C, D, E) → a, faceABCD, edgeAE, edgeBE, edgeCE, edgeDE, faceABE, faceBCE, faceCDE, faceADE, edgeAB, edgeBC, edgeCD, edgeAD
  3. IntersectPath(b, a) → poly1, F, g, G, H, I, J, c, d, e, f
  4. OrthogonalLine(E, xOyPlane) → h
  5. Intersect(h, xOyPlane) → K
  6. Intersect(h, b) → L
  7. Segment(E, K) → i
  8. Distance(E, L) → distanceEL
  9. Distance(E, K) → distanceEK
  10. PointIn(faceABCD) → PointfaceABCD
  11. PointIn(poly1) → Pointpoly1
  12. Segment(E, L) → j
  13. OrthogonalLine(L, d, space) → k
  14. OrthogonalLine(K, edgeBC, space) → l
  15. Intersect(l, edgeAD) → M
  16. Intersect(k, f) → N
  17. Angle(M, K, E) → α
  18. Angle(N, L, E) → β
  19. Distance(E, L) → EL
  20. Distance(E, K) → EK