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