We consider the Dirichlet problem for the semilinear equation $\Delta u+f(u)=0$  on a  bounded domain $\Omega\subset \mathbb R^N$. We assume that $\Omega$ is convex in a direction $e$ and symmetric  about the hyperplane $H=\{x\in\mathbb R^N: x\cdot e=0\}$. It is known that if $N\ge 2$ and $\Omega$ is of class $C^2$, then any nonzero nonnegative solution is necessarily strictly positive and, consequently, it  is reflectionally symmetric about $H$ and decreasing in the direction $e$ on the set $\{x\in\Omega: x\cdot e>0\}$.  In this paper, we prove the same result for a large class of nonsmooth planar domains. In particular,  the result is valid if any of the following additional conditions on $\Omega$ holds:

  (i) $\Omega$ is convex (not necessarily symmetric) in the direction perpendicular to $e$, 

 (ii) $\Omega$ is strictly convex in the direction $e$,

(iii) $\Omega$ is piecewise-$C^{1,1}$.