cheer up vs triumph

cheer up is not a noun while triumph is a noun.

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

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

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

cheer up (noun)	triumph (noun)
	a successful ending of a struggle or contest
	the exultation of victory

cheer up (verb)	triumph (verb)
become cheerful	dwell on with satisfaction
cause (somebody) to feel happier or more cheerful	to express great joy
	prove superior
	be ecstatic with joy