CMOQR 2018 Problem 2

We call a pair of polygons, $p$ and $q$ , nesting if we can draw one inside the other, possibly after rotation and/or reflection; otherwise we call them non-nesting.

Let $p$ and $q$ be polygons. Prove that if we can find a polygon $r$ , which is similar to $q$ , such that $r$ and $p$ are non-nesting if and only if $p$ and $q$ are not similar.