I came across the definition below to see how $n$-sided polygons are defined to be congruent.
Definition: It is said that two $n-$gons are congruent iff their corresponding sides and corresponding angles are congruent.
$\bullet$ It can be proven that any $n-$sided polygon can be partitioned into $n-2$ triangles by triangulation.
$\bullet$ I personally would think the definition of congruent $n-$gons would be that two $n-$sided polygons are congruent iff each polygon can be partitioned into triangles in a way that leads two an isomorphism between their graphs as well as a correspondence of congruent triangles.
The reason I would think this is because the two polygons would be connected the same way by congruent triangles making the shapes themselves congruent.
$\textbf{Question:}$ Is there a relationship between these ideas? Is there any intuition behind how congruent polygons are defined? My concern is how this definition could imply two congruent shapes can be partitioned the same way by triangles.