trivalry means: Tri-val-ry trahy-vuh l-ree -noun, plural-ries 1. A person who tries to be equal to or better another while also trying to beat a third party, or pursues the same goal as the others; a competitor. 2. A person that is equal or nearly equal to another, and/or third entities in particular aspects. 3. The action, position or relationship of a competitor or rivals. Competition: Trivalry between Calgary and Edmonton. (in Community Dictionary, added by Johanna Oliver)