Congruence classes of triangles in ${\mathbb{F}}_p^2$

In this short note, we give a lower bound on the number of congruence classes of triangles in a small set of points in ${\mathbb{F}}_p^2$. More precisely, for $\mathcal{A}\subset {\mathbb{F}}_p^2$ with $\mathrm{\mid }\mathcal{A}\mathrm{\mid }\le p^{2\mathrm{/}3}$, we prove that the number of congruence classes of triangles determined by points in $\mathcal{A}\times \mathcal{A}$ is at least $\mathrm{\mid }\mathcal{A}{\mathrm{\mid }}^{7\mathrm{/}2}$. This note is not intended for journal publication.