Meaning
Shameless / To have some nerve
Example
Carlos é tão cara de pau. Ele está paquerando a mulher do chefe!
Carlos is so shameless. He's flirting with the boss's wife!
Origin
The origin is uncertain. 'Cara' is 'face'; 'pau' is 'wood.' The image — a wooden, unreactive face — is close to 'cara de pau' (shameless) but with the nuance of 'nerve' and 'audacity.' Some link it to wooden theatrical masks.
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More idioms
Acertar na moscaTo guess correctly / To hit the nail on the headAmigo da onçaA fake/false friendAndar na linhaTo toe the line / To behave properlyArmar um barracoTo cause a public sceneRodar a baianaTo cause a public scene / To go ballisticArrumar sarna pra se coçarTo ask for troubleArrastar as asasTo hit on someone / To flirtAbrir o jogoTo come clean / To open upArregaçar as mangasTo roll up one's sleeves / To get to workAgarrar com unhas e dentesTo hold on for dear life / To seize an opportunity