Etymology
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miter (n.1)

in reference to a type of head-dress, an alternative spelling of mitre (see -re).

miter (n.2)

in carpentry, "a joint at a 45 degree angle," 1670s, of uncertain origin, perhaps from mitre, via notion of joining of the two peaks of the folded cap. As a verb, to make or join with a miter-joint," from 1731. Related: Mitered. Miter-box is attested from 1670s.

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Definitions of miter
1
miter (v.)
bevel the edges of, to make a miter joint;
miter (v.)
confer a miter on (a bishop);
miter (v.)
fit together in a miter joint;
2
miter (n.)
joint that forms a corner; usually both sides are bevelled at a 45-degree angle to form a 90-degree corner;
Synonyms: miter joint / mitre joint / mitre
miter (n.)
the surface of a beveled end of a piece where a miter joint is made;
he covered the miter with glue before making the joint
Synonyms: mitre
miter (n.)
a liturgical headdress worn by bishops on formal occasions;
Synonyms: mitre
From wordnet.princeton.edu