Similar polygon properties

Dependencies: SSS and SAS similarity tests, Similar perimeter ratio = k, Similar area ratio = k².

Statement

Suppose convex polygons $P = V_0 V_1 \cdots V_{n-1}$ and $P' = V_0' V_1' \cdots V_{n-1}'$ are similar with similarity ratio

Then the three groups of corresponding geometric quantities satisfy the following proportionality relations:

In other words, for similar polygons, corresponding side lengths are in ratio $k$, perimeters are in ratio $k$, and areas are in ratio $k^2$. This extends "similarity = same shape with adjustable scale" from triangles to arbitrary convex $n$-gons.