In order to identify barre chords in ex. 1 we need to learn the notes on the 6th string. The 6th string (big string) is the root note that identifies the chord.

ex.1 barre chords with the root on the 6 string:

In order to identify barre chords in ex. 2 we need to learn the notes on the 5th string. The 5th string is the root note that identifies the chord.

ex.2 barre chords with the root note on the 5 string: