o seu: the Polite Your
When you address someone as você, o senhor or a senhora, the matching possessive is seu — with the article, agreeing with the THING owned, like every possessive you know:
| What is your (formal) name? | Qual é o seu nome? |
| Do you (formal) have your ticket, sir? | O senhor tem o seu bilhete? |
| You (formal) have your key here, madam. | A senhora tem a sua chave aqui. |
| Teacher, your book is on the table. | Professora, o seu livro está na mesa. |
Why Not his/her?
On paper seu also means his or her — but you learned the Portuguese solution to that ambiguity long ago: dele / dela. In Portugal, o carro dele is his car and o seu carro is YOUR (polite) car. Keep that division and you will never be misunderstood.
o vosso: Your (to a Group)
Speaking to several people (vocês), the possessive is — article included, agreeing with the thing owned:your (plural, of vocês; forms: vosso, vossa, vossos, vossas) vosso
| Your (plural) house is beautiful. | A vossa casa é bonita. |
| Does your (plural) teacher speak English? | O vosso professor fala inglês? |
| Your (plural) books are on the table. | Os vossos livros estão na mesa. |
The full family, side by side: o meu, o teu, o seu, o nosso, o vosso — and dele/dela/deles/delas doing third-person duty from the other direction.
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