Characterizations by automorphism groups of some rank 3 buildings, II : a half strongly-transitive locally finite triangle building is a Bruhat-Tits building

We complete the proof of the fact that every locally finite triangle building Delta with a half strongly-transitive automorphism group G (e.g., this happens when Delta is defined via a (B, N)-pair in G) is a Bruhat-Tits building associated with a classical linear group over a locally finite local skewfield