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Perder vs. extraviar

While both verbs refer to the act of losing something, the choice between perder and extraviar depends heavily on the context and the level of formality. Perder is the universal term for losing anything, whereas extraviar is specific to items going astray during transport or administrative processes.

Perder

A1
This is the standard, everyday verb used when you lose or misplace an item regardless of the cause. It implies that the possessor no longer knows where the object is, whether it was left behind, dropped, or simply vanished inside one's home.
Eu perdi as chaves do carro ontem à noite.
(I lost the car keys last night.)
Ela acha que perdeu a carteira no supermercado.
(She thinks she lost her wallet at the supermarket.)
Cuidado para não perder o seu passaporte.
(Be careful not to lose your passport.)
Ele vive a perder os óculos pela casa.
(He is always misplacing his glasses around the house.)
Nós perdemos o controle remoto da televisão de novo.
(We misplaced the television remote control again.)

Extraviar

B2
This verb is more formal and technical, literally meaning to go astray or off-course. It is used almost exclusively when items are lost during transit, shipping, or within a bureaucratic system, such as mail, luggage, or official files.
A companhia aérea extraviou a minha bagagem durante a conexão.
(The airline misplaced my luggage during the connection.)
O correio informou que a carta se extraviou.
(The post office informed that the letter got lost.)
Documentos importantes foram extraviados no arquivo morto.
(Important documents were misplaced in the dead archive.)
A transportadora não se responsabiliza por mercadorias extraviadas.
(The carrier is not responsible for misplaced merchandise.)
O pacote acabou se extraviando no caminho para o Brasil.
(The package ended up getting lost on the way to Brazil.)

Summary

In short, use perder for all general, personal situations where you cannot find an object. Use extraviar in formal contexts, specifically when talking about logistic failures involving mail, cargo, luggage, or documents handled by a third party.