  The cosmological principle is one of the fundamental assumptions of the
standard model of Cosmology (SCM), and it allow us to describe cosmic distances
and clocks by using the Friedmann-Lema$\rm{\hat{{\i}}}$tre-Roberton-Walker
(FLRW) metric. Thus, it is essential to test the FLRW metric with cosmological
observations to verify the validity of the SCM. In this work, we perform tests
of the FLRW metric by comparing the observational comoving angles between the
Hubble $H(z)$ and angular Baryon Acoustic Oscillation (BAO) measurements. The
Gaussian process is employed to reconstruct the Hubble $H(z)$ measurements and
the angular diameter distance (ADD) from the transversal BAO data. A
non-parametric method is adopted to probe the possible deviations from the FLRW
metric at any redshift by comparing the comoving distances from the
reconstructed Hubble $H(z)$ measurements with the ADD reconstructed from the
transversal BAO data. Then, we propose two types of parameterizations for the
deviations from the FLRW metric, and test the FLRW metric by using the priors
of specific sound horizon scales. To avoid the bias caused by the prior of a
specific sound horizon scale, we perform the consistency test with a flat prior
of the sound horizon scale. We find that there a concordance between the FLRW
metric and the observational data by using parametric and non-parametric
methods, and the parameterizations can be employed to test the FLRW metric in a
new way independent of the sound horizon scale.
