Die Vorhänge sind zugezogen.

English Translation

The curtains are closed.

When talking about closed/drawn/pulled curtains this sentencenkeads me to beleive the only legitimate verb to use is “zuziehen”?

Yes, “zugezogen” is the past participle of “zuziehen”, used as an adjective. It’s literally “pulled to a closed state”.

German makes the same distinction between an adjective and the passive as english:
Die Vorhänge sind zugezogen. - The curtains are closed. (in a closed state)
Die Vorhänge wurden zugezogen. - The curtains have been closed. (someone closed them)

As for the question whether “zuziehen” is the only viable verb here, you can just use “zu”:
Die Vorhänge sind zu.

But yes, there is not much else. “Schließen” doesn’t fit. That only works for doors and windows.

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