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Right and Oblique Pyramids Comparison

Right and Oblique Pyramids Comparison
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2017-04-04 22:46
PolygonCoordinate GeometrySolid GeometryGeometric Construction
①This GeoGebra example visually demonstrates the structural differences between a right pyramid (apex directly above the base center) and an oblique pyramid (apex offset from the center) in 3D space. ②Core mathematical concepts include the definition of pyramids, how the apex projection affects pyramid type, relationships between lateral faces and base polygon, and spatial concepts of perpendicularity and obliqueness. ③Construction highlights: uses Polygon to create the base, OrthogonalLine and Intersect to find the base center and perpendicular line, Plane and Point to place the apex, Pyramid to generate the solid, and PointIn along with multiple auxiliary points (A, B, C, D, E, F, G, H) and face/edge objects (faceABG, edgeAG, etc.) for complete modeling. ④Suitable for high school solid geometry or introductory university spatial geometry, helping students understand criteria for right vs. oblique pyramids and enhance spatial visualization skills.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 5) → poly1, f, g, h, i, j, C, D, E
  2. OrthogonalLine(D, f) → k
  3. OrthogonalLine(C, j) → l
  4. Intersect(k, l) → F
  5. Plane(poly1) → a
  6. OrthogonalLine(F, a) → m
  7. Point(m) → G
  8. Pyramid(poly1, G) → b, faceABG, edgeEG, faceBCG, faceCDG, faceDEG, faceAEG, edgeAG, edgeBG, edgeCG, edgeDG
  9. Plane(G, a) → c
  10. PointIn(c) → H
  11. Pyramid(poly1, H) → d, faceABH, edgeEH, faceBCH, faceCDH, faceDEH, faceAEH, edgeAH, edgeBH, edgeCH, edgeDH

AI Drawing Prompt Reference

Draw a regular pentagon as the base in 3D space. Find its center and construct a line perpendicular to the base through the center. Place a point on this perpendicular line as the apex of a right pyramid, then connect this apex to all base vertices to form the right pyramid. Next, place another point above the base but offset from the center, not on the perpendicular line, as the apex of an oblique pyramid. Connect this second apex to all base vertices to form the oblique pyramid. Both pyramids share the same pentagonal base, visually contrasting the right pyramid's apex directly above the center with the oblique pyramid's apex shifted to the side.
The prompt above was compiled from the original drawing commands and is for reference only.