Monday, July 13, 2015

Unizor - Geometry3D - Prisms - Mini Theorems 1

Unizor - Creative Minds through Art of Mathematics - Math4Teens

Mini Theorem A
If a directrix of a cylindrical surface is a straight line non-parallel to a generatrix, this surface is a plane.

Mini Theorem B
If a directrix of a cylindrical surface is a polygon ABCDE lying within a plane γ non-parallel to a generatrix, then any other plane δ, parallel to plane γ, intersects a given cylindrical surface along a polygon A'B'C'D'E' congruent to polygon-directrix ABCDE.

Corollary 1
Immediate consequence of the above theorem is that two polygons that are the bases of a prism are congruent with correspondingly parallel and equal edges and correspondingly equal angles.

Corollary 2
Each side face of a prism is a parallelogram.

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