From Halopedia, the Halo wiki
Triage, along with the barracks, mess hall, and the Officer's Quarters, is a building included in any military camp or base, and is used to store medical supplies as well as treat injuries. Commonly, the Corpsman will also have his living quarters in triage.
In hospitals and emergency medical facilities, triage is the process of prioritizing patients based on how severe their injuries or wounds are so as to treat as many patients as possible with minimum casualties when resources are insufficient for all to be treated immediately. The term originates from the French verb trier, meaning "to sort, sift or select". Such a triage was set up in the New Alexandria cargo port during the Siege of New Alexandria.
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