  Nodal angle resolved photoemission spectra taken on overdoped
La$_{1.77}$Sr$_{0.23}$CuO$_4$ are presented and analyzed. It is proven that the
low-energy excitations are true Landau Fermi-liquid quasiparticles. We show
that momentum and energy distribution curves can be analyzed self-consistently
without quantitative knowledge of the bare band dispersion. Finally, by
imposing Kramers-Kronig consistency on the self-energy $\Sigma$, insight into
the quasiparticle residue is gained. We conclude by comparing our results to
quasiparticle properties extracted from thermodynamic, magneto-resistance, and
high-field quantum oscillation experiments on overdoped
Tl$_2$Ba$_2$CuO$_{6+\delta}$.
