Unizor - Geometry2D - Similarity - Segments
Channel: Zor Shekhtman on UNIZOR Education
Date: 2012-05-18

While angles are preserved by scaling, segments, obviously, are not. In particular, segments connecting the center of scaling Q with any point on a plane M are stretching or contracting during the transformation of scaling along the line from Q to M. By definition of scaling, all such segments with one endpoint at the center of scaling Q are stretching or contracting by the same factor, which is a factor of scaling. This is not a theorem, it's a definition of scaling.
We will prove now that any segment, not necessarily connecting a center of scaling with some point, is also stretching or contracting by the same factor of scaling.