Old English hæt "hat, head covering," from Proto-Germanic *hattuz "hood, cowl" (cf. Frisian hat, Old Norse hattr), from PIE root *kadh- "cover, protect" (cf. Lithuanian kudas "tuft or crest of a bird," Latin cassis "helmet"). Now, "head covering with a more or less horizontal brim." To throw one's hat in the ring was originally (1847) to take up a challenge in prize-fighting. To eat one's hat is said to have been originally To eat Old Rowley's [Charles II's] hat.
To lie and exaggerate; talk nonsense; bullshit
[1887+; said to be fr the deceptive demeanor of men who hold their hats over their faces on entering church, and are supposed to be praying]
A condom (1990s+ Teenagers)
brass hat, gimmie hat, hard hat, here's your hat what's your hurry, high-hat, knock something into a cocked hat, old hat, party hat, pass the hat, shit in your hat, straw hat, talk through one's hat, throw one's hat in the ring, tin hat, under one's hat, wear two hats, white hat, wool hat