  We prove that any metric space $X$ homeomorphic to $\mathbb{R}^2$ with
locally finite Hausdorff 2-measure satisfies a reciprocal lower bound on
modulus of curve families associated to a quadrilateral. More precisely, let $Q
\subset X$ be a topological quadrilateral with boundary edges (in cyclic order)
denoted by $\zeta_1, \zeta_2, \zeta_3, \zeta_4$ and let $\Gamma(\zeta_i,
\zeta_j; Q)$ denote the family of curves in $Q$ connecting $\zeta_i$ and
$\zeta_j$; then $\text{mod} \Gamma(\zeta_1, \zeta_3; Q) \text{mod}
\Gamma(\zeta_2, \zeta_4; Q) \geq 1/\kappa$ for $\kappa = 2000^2\cdot
(4/\pi)^2$. This answers a question concerning minimal hypotheses under which a
metric space admits a quasiconformal parametrization by a domain in
$\mathbb{R}^2$.
