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Truncated pyramid

Lecture






Theorem

The plane intersecting the pyramid and parallel to its base, cuts off a similar pyramid.

  Truncated pyramid

Evidence

Let S be the vertex of the pyramid, A be the vertex of the base, and A` be the intersection point of the section plane with the side edge SA. Let us pyramid the homothety transformation relative to the vertex S with the homothety coefficient

  Truncated pyramid

With this homothety, the base plane goes into a parallel plane passing through point A`, i.e. in the cutting plane, and consequently, the whole pyramid is in the part that is cut off by this plane. Since the homothety is a similarity transformation, the cut-off part of the pyramid is a pyramid similar to this one. The theorem is proved.
created: 2014-10-05
updated: 2021-03-13
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Stereometry

Terms: Stereometry