Congruent and Similar Solids

Okay, we can now extend this. Consider two solids which have the same number of faces, vertices, and edges, and have the same angles between each set of sides. The corresponding sides are then in the same ratio of lengths. These two solids are said to be similar.

For example, consider two regular tetrahedra, one of whose sides all have length $1$, and the other all of whose sides have length $3$. These two tetrahedron are similar.

Congruent solids are a special subset of similar solids. Specifically, they are solids that are exactly the same; i.e. the similarity ratio is $1$.