  The quantum geometry has significant consequences in determining transport
and optical properties in quantum materials. Here, we use a semiclassical
formalism coupled with perturbative corrections unifying the nonlinear
anomalous Hall effect (NLAHE) and nonreciprocal magnetoresistance (NMR,
longitudinal resistance) from the quantum geometry. In the dc limit, both
transverse and longitudinal nonlinear conductivities include a term due to the
normalized quantum metric dipole. The quantum metric contribution is intrinsic
and does not scale with the quasiparticle lifetime. We demonstrate the
coexistence of a NLAHE and NMR in films of the doped antiferromagentic
topological insulator MnBi$_2$Te$_4$. Our work indicates that both longitudinal
and transverse nonlinear transport provide a sensitive probe of the quantum
geometry in solids.
