  Let $P$ be a set of $N$ points in the Euclidean plane, where a positive
proportion of points lies off a single straight line. This note points out two
facts concerning the number of equivalence classes of triangles that $P$
determines, namely that (i) $P$ determines $\Omega(N^2)$ different equivalence
classes of congruent triangles, and (ii) $P$ determines $\Omega(\frac{N^2}{\log
N})$ different equivalence classes of similar triangles. The first fact follows
from the recent theorem by Guth-Katz on point-line incidences in $\R^3$. The
second one, perhaps not so well known, is due to Solymosi and Tardos.
