Aquelas são as portas, através das quais fomos para o salão.

Questions & Answers about Aquelas são as portas, através das quais fomos para o salão.

Why does the sentence use das quais instead of just as quais?
The phrase for "through" is actually através de. When linking it to the relative pronoun as quais (which refers to the feminine plural as portas), the preposition de combines with as to make das. So, através de + as quais becomes através das quais.
Could I just use que here, like "através de que"?
No, because através de contains a multi-syllable word (através). In Portuguese, you can generally only use the simple relative pronoun que after short, single-syllable prepositions (like a, em, or com). For longer prepositions, you have to use a form of o qual, which is why we use as quais here.
Why use aquelas at the beginning instead of essas?
Both words mean "those" and match the feminine plural noun portas, but aquelas is used when the objects are physically far away from both the speaker and the person they are talking to. If the doors were close to the listener, you would use essas.
What is the difference between saying fomos para o salão and fomos ao salão?
When using the verb ir (to go), the preposition para usually implies moving to a final destination or staying for a while. Using a (which combines with o to make ao) would imply a very brief visit, like just popping your head into the hall and leaving again right away.

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