SG. 1 Given some triangles with side lengths $a \mathrm{~cm}, 2 \mathrm{~cm}$ and $b \mathrm{~cm}$, where $a$ and $b$ are integers and $a \leq 2 \leq b$. If there are $q$ non-congruent classes of triangles satisfying the above conditions, find the value of $q$.
When $a=1$, possible $b=2$
When $a=2$, possible $b=2$ or 3
$$
\therefore q=3
$$