In Spanish, to express that something is considered as "adjective or participle" we use this structure:
Dar algo/alguien por + participle/adjective
For example:
Lo dieron por muerto pero nunca apareció su cuerpo.They gave him up for dead but his body never showed up.
Decía tantas barbaridades que la daban por loca.She said so many outrageous things that they considered her crazy.
Sometimes the verb dar is reflexive:
darse por + adjective/participle
For example:
Note that the adjective/participle needs to agree with the noun/person it is referring to.
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Examples and resources
Los clientes se dieron por satisfechos con el descuento que les hicimos.The clientes considered themselves satisfied with the discount we gave them.
Probamos una y otra vez y al final lo dimos por imposible.We tried over and over and in the end we gave it up as impossible.
Decía tantas barbaridades que la daban por loca.She said so many outrageous things that they considered her crazy.