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3D Pythagorean Theorem Demo

3D Pythagorean Theorem Demo
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2018-01-21 04:21
VectorSolid GeometryOptimizationGeometric Construction
This example demonstrates the 3D Pythagorean Theorem geometrically in space, constructing a right triangular prism to show the volume relationship. Key math concepts include solid geometry, Pythagorean theorem, volume calculation, and spatial vectors. Construction highlights from the GeoGebra command summary involve commands like Line, Point, OrthogonalLine, Intersect, Polygon, Prism, Segment, and objects such as A, B, C, D, etc. Suitable for high school students and math enthusiasts studying applications of spatial vectors in 3D geometry.

GeoGebra Commands & Parameters

  1. Line(A, B) → f
  2. Point(f) → C
  3. Point(f) → D
  4. OrthogonalLine(C, f) → g
  5. OrthogonalLine(D, f) → h
  6. Point(g) → E
  7. OrthogonalLine(E, g) → i
  8. Intersect(i, h) → F
  9. Polygon(C, E, F, D) → c1, c, e, f_1, d
  10. OrthogonalLine(C, c1) → j
  11. Point(j) → G
  12. Prism(c1, G) → a, H, aristaEH, aristaFI, aristaDJ, aristaGH, aristaHI, aristaIJ, aristaGJ, I, J, caraCEHG, caraEFIH, caraDFIJ, caraCDJG, caraGHIJ, aristaCG
  13. Segment(D, H) → k
  14. Segment(E, D) → l

AI Drawing Prompt Reference

Draw a 3D right triangular prism to demonstrate the Pythagorean theorem geometrically, highlighting the volume relationship with its base and sides, constructed through lines and points defining the prism's shape and emphasizing key geometric relationships and vector applications in space.
The prompt above was compiled from the original drawing commands and is for reference only.