An instrument to produce fire

safety match, sulphur match, matchstick, fuse, lucifer, locofoco*; see also light 3.

An article that is like another

peer, equivalent, mate, analogue, counterpart, approximation; see also equal.

A formal contest

race, event, rivalry; see competition 2, sport 3.

A marriage or engagement

mating, union, espousal; see marriage 2.

To find or make equals

equalize, liken, equate, make equal, pair, coordinate, level, even, match up, balance, mate, marry, unite; see also equal.

To be alike

harmonize, suit, be twins, be counterparts, be doubles, match with, check with, go together, go with, rhyme with, take after; see also agree, resemble.

Antonyms differ*, be unlike, clash. *

To meet in contest

equal, keep pace with, run side by side, come up with, be on a level with, cope with, meet, compete with; see also rival.