  We study the $D_s^+\to \pi^+(a_0(980)^0\to)\pi^0\eta$,
$\pi^0(a_0(980)^+\to)\pi^+\eta$ decays, which have been recently measured by
the BESIII collaboration. We propose that $D_s^+\to
\pi^{+(0)}(a_0(980)^{0(+)}\to)\pi^{0(+)}\eta$ receives the contributions from
the triangle rescattering processes, where $M^0$ and $\rho^+$ in $D_s^+\to M^0
\rho^+$, by exchanging $\pi^{0(+)}$, are formed as $a_0(980)^{0(+)}$ and
$\pi^{+(0)}$, respectively, with $M^0=(\eta,\eta')$. Accordingly, we calculate
that ${\cal B}(D_s^+\to a_0(980)^{0(+)}\pi^{+(0)})=(1.7\pm 0.2\pm 0.1)\times
10^{-2}$ and ${\cal B}(D_s^+\to
\pi^{+(0)}(a_0(980)^{0(+)}\to)\pi^{0(+)}\eta)=(1.4\pm 0.1\pm 0.1)\times
10^{-2}$, being consistent with the data.
