cheer vs triumph

cheer and triumph both are nouns.

Word	Noun	Adjective	Verb	Adverb
cheer	Yes	No	Yes	No
triumph	Yes	No	Yes	No

As verbs, triumph is a hyponym of cheer; that is, triumph is a word with a more specific, narrower meaning than cheer:

Other hyponyms of cheer include exuberate, exult, jubilate, rejoice, buoy up, lighten, lighten up.

cheer (noun)	triumph (noun)
the quality of being cheerful and dispelling gloom	a successful ending of a struggle or contest
a cry or shout of approval	the exultation of victory

cheer (verb)	triumph (verb)
become cheerful	dwell on with satisfaction
spur on or encourage especially by cheers and shouts	to express great joy
show approval or good wishes by shouting	prove superior
cause (somebody) to feel happier or more cheerful	be ecstatic with joy
give encouragement to