Problem

Source: Canada RepĂȘchage 2018/2

Tags: geometry, geometric transformation, rotation, reflection



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.