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Cross Section of a Triangular Prism

Cross Section of a Triangular Prism
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2020-03-02 00:10
PolygonAngleVectorSolid GeometryGeometric Construction
In collections Cross Sections
This example demonstrates the cross-section of a triangular prism, highlighting its geometric properties. Key math concepts include solid geometry, polygons, angle calculations, and vector operations. The construction utilizes GeoGebra commands like Point, Polygon, Prism, Plane, Circle, Line, Intersect, OrthogonalLine, CircleArc, Segment, OrthogonalPlane, and IntersectPath. Ideal for high school students and math enthusiasts studying 3D geometry and geometric constructions.

GeoGebra Commands & Parameters

  1. Point(xAxis) → V
  2. Polygon(U, V, W) → t1, w, u, v
  3. Prism(t1, a) → ThePrism, Z, edge2, edge3, edge5, edge4, A_1, B_1, face2, face4, face3, face1, edgeUZ, edge1
  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(ThePrism) → SliceChooser
  23. OrthogonalPlane(SliceChooser, NormalSeg) → PerPenPlane
  24. IntersectPath(PerPenPlane, ThePrism) → CrossSection, D, l, E, F, G, H, f, i, j, k

AI Drawing Prompt Reference

Draw a triangular prism with a triangular base and adjustable height. Place a movable point inside the prism and construct a plane through this point that is perpendicular to a normal direction, where the normal direction is controlled by a point on an auxiliary circle outside the prism. This plane intersects the prism to form a polygonal cross-section that changes as the control point moves. Additionally, construct an auxiliary plane determined by three points on the coordinate axes, and draw a small circle and a line on it to illustrate angle relationships. The overall figure includes the prism, the cross-section polygon, the auxiliary plane, the circle, the line, and several key points, demonstrating concepts of cross-sections and angles in solid geometry.
The prompt above was compiled from the original drawing commands and is for reference only.