  We show how the theory of the critical behaviour of $d$-dimensional polymer
networks gives a scaling relation for self-avoiding {\em bridges} that relates
the critical exponent for bridges $\gamma_b$ to that of terminally-attached
self-avoiding arches, $\gamma_{1,1},$ and the {correlation} length exponent
$\nu.$ We find $\gamma_b = \gamma_{1,1}+\nu.$ We provide compelling numerical
evidence for this result in both two- and three-dimensions. Another subset of
SAWs, called {\em worms}, are defined as the subset of SAWs whose origin and
end-point have the same $x$-coordinate. We give a scaling relation for the
corresponding critical exponent $\gamma_w,$ which is $\gamma_w=\gamma-\nu.$
This too is supported by enumerative results in the two-dimensional case.
