  A graph is called equimatchable if all of its maximal matchings have the same
size. Frendrup et al. [8] provided a characterization of equimatchable graphs
with girth at least $5$. In this paper, we extend this result by providing a
complete structural characterization of equimatchable graphs with girth at
least $4$, i.e., equimatchable graphs with no triangle, by identifying the
equimatchable triangle-free graph families. Our characterization also extends
the result given by Akbari et al. in [1], which proves that the only connected
triangle-free equimatchable $r$-regular graphs are $C_5$, $C_7$ and $K_{r,r}$,
where $r$ is a positive integer. Given a non-bipartite graph, our
characterization implies a linear time recognition algorithm for triangle-free
equimatchable graphs.
