Baryon acoustic oscillation (BAO) analyses usually report the anisotropic shift parameters ${\alpha }_{\perp }(z)$ and ${\alpha }_{\parallel }(z)$ relative to a fiducial cosmology, and these quantities are primarily used for cosmological parameter inference. Here we show that they can also be used to construct a direct internal consistency test of the background geometry. In particular, we derive a new null test of flat Friedmann-Lemaître-Robertson-Walker (FLRW) geometry written entirely in terms of the reported BAO shift parameters. The test is calibration free: the sound-horizon ratio $r_{\mathrm{d}}/r_{\mathrm{d}}^{\mathrm{fid}}$ cancels identically, so the relation is independent of the absolute BAO scale, and is also fiducial invariant, preserved under exact remapping between any two flat fiducial cosmologies, so the result is not an artifact of any particular survey choice. We also derive a calibration-free reconstruction of the deceleration parameter $q(z)$ from the radial BAO sector. Applying these results to anisotropic DESI DR2 BAO measurements, we find no evidence for a breakdown of the flat-FLRW distance relation within current uncertainties. Our results show that anisotropic BAO measurements already provide a nontrivial internal geometric consistency test before performing any model fit.

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• Cosmology
• Dark energy
• Large scale structure of the Universe