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Triangular Pyramid Cross Section

Triangular Pyramid Cross Section
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2020-03-04 22:21
Coordinate GeometrySolid GeometryGeometric Construction
In collections Cross Sections
This example demonstrates the cross-section of a triangular pyramid when intersected by a plane. It involves core concepts in solid geometry, including the intersection of a plane with a pyramid and the resulting geometric shapes. The construction utilizes various GeoGebra commands and objects such as Point, Polygon, Pyramid, Plane, Circle, Line, Intersect, OrthogonalLine, CircleArc, Segment, OrthogonalPlane, and IntersectPath. It is suitable for high school students and mathematics enthusiasts exploring spatial geometry and cross-section problems.

GeoGebra Commands & Parameters

  1. Point(xAxis) → V
  2. Polygon(U, V, W) → t1, w, u, v
  3. Pyramid(t1, m) → ThePyra, P, facePUV, facePVW, facePUW, edgePU, edgePV, edgePW
  4. Point(xAxis) → A
  5. Point(zAxis) → O
  6. Point(xAxis) → K
  7. Point(yAxis) → J
  8. Point(xAxis) → I
  9. Plane(I, K, O) → b
  10. Plane(I, J, K) → p
  11. PointIn(b) → CenterOfNormalAngle
  12. Circle(CenterOfNormalAngle, 0.25, b) → d
  13. Line(CenterOfNormalAngle, xAxis) → g
  14. Point(yAxis) → B
  15. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  16. Intersect(xAxis, yAxis) → M
  17. OrthogonalLine(CenterOfNormalAngle, g, b) → h
  18. Intersect(g, d) → i_1, i_2
  19. CircleArc(CenterOfNormalAngle, i_1, i_2, b) → ArcForPlaneAngle
  20. Point(ArcForPlaneAngle) → NormalAngleHandle
  21. Segment(CenterOfNormalAngle, NormalAngleHandle) → NormalSeg
  22. PointIn(ThePyra) → SliceChooser
  23. OrthogonalPlane(SliceChooser, NormalSeg) → PerPenPlane
  24. IntersectPath(PerPenPlane, ThePyra) → poly1, D, E, F, R, f, i, j, r