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Projection of Apex of Right Pyramid by lowaiyip

Projection of Apex of Right Pyramid by lowaiyip
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2016-02-02 12:03
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the projection of the apex of a right pyramid onto a plane, illustrating key geometric concepts such as projection, orthogonal lines, midpoints, angle bisectors, and tetrahedral geometry. It utilizes GeoGebra commands like Intersect, Point, Cone, Circle, Pyramid, OrthogonalLine, Midpoint, Line, AngularBisector, Segment, and Angle to construct the visualization. Suitable for high school and advanced learners in solid geometry and analytical geometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → circumcentre
  2. Point(zAxis) → V
  3. Cone(circumcentre, V, 1) → a, c, b
  4. Point(c) → A
  5. Point(c) → B
  6. Point(c) → C
  7. Circle(A, C, B) → e
  8. Pyramid(C, A, B, V) → d, faceABC, edgeBV, faceACV, faceABV, faceBCV, edgeAC, edgeAB, edgeBC, edgeCV, edgeAV
  9. OrthogonalLine(B, edgeAC, xOyPlane) → f
  10. OrthogonalLine(A, edgeBC, xOyPlane) → g
  11. Intersect(f, g) → orthocentre
  12. Midpoint(edgeBC) → D
  13. Midpoint(edgeAC) → E
  14. Line(B, E) → h
  15. Line(A, D) → i
  16. Intersect(h, i) → centroid
  17. AngularBisector(edgeAC, edgeAB) → j, k
  18. AngularBisector(edgeAC, edgeBC) → l, m
  19. Intersect(k, m) → incentre
  20. Intersect(yAxis, zAxis) → V'
  21. Segment(V', V) → p
  22. Segment(V', A) → q
  23. Angle(V, V', A) → α
  24. OrthogonalLine(C, edgeAV, space) → s
  25. OrthogonalLine(B, edgeAV, space) → t