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Diagonal Hint for a Rectangular Prism

Diagonal Hint for a Rectangular Prism
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2017-11-26 09:07
VectorSolid GeometryGeometric Construction
In collections GeoGebra 3D & AR: Geometry Resources & Challenges
This example demonstrates how to dynamically calculate the diagonal length of any rectangular prism. It involves core math concepts like solid geometry, spatial vectors, and the extension of the Pythagorean theorem. Construction uses GeoGebra commands such as Prism, Dilate, Polygon, Segment, and Angle to build the prism and compute its diagonals. Suitable for high school geometry teaching or self-learning to understand spatial geometric calculations.

GeoGebra Commands & Parameters

  1. Prism(G, F, A, I, H) → s, J, edgeFG, edgeAF, edgeAI, edgeGI, edgeGH, edgeFJ, edgeAK, edgeIL, edgeHJ, edgeJK, K, edgeKL, edgeHL, L, faceAFGI, faceFGHJ, faceAFJK, faceAILK, faceGHLI, faceHJKL
  2. Dilate(A, If[9 < animate ≤ 10, 10 - animate, 0], F) → A'
  3. Polygon(A, F, G) → t1, g, a_1, f_1
  4. Segment(A, A') → h
  5. Dilate(F, If[10 < animate ≤ 11, 11 - animate, 0], G) → F'
  6. Segment(F, F') → j
  7. Angle(G, F, A) → α
  8. Dilate(G, If[11 < animate ≤ 12, 12 - animate, 0], A) → G'
  9. Segment(G, G') → k
  10. Dilate(G, If[13 < animate ≤ 14, 14 - animate, 0], H) → G'_1
  11. Segment(G, G'_1) → l
  12. Dilate(H, If[14 < animate ≤ 15, 15 - animate, 0], A) → G'_2
  13. Segment(H, G'_2) → m
  14. Angle(H, G, A) → β
  15. Polygon(H, G, A) → t2, a_2, h_1, g_1