I have to write the sentence:
En chemin, elle rencontre un loup qui a faim.
in the past. Should I translate to "elle a rencontré" or "elle a rencontrée" and why?
En chemin, elle a rencontré(e) un loup qui avait a faim.
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Elle a rencontré
the always valid rule is that with avoir for auxiliary, there is no agreement, as opposed to être. Here, a is from avoir, therefore no need to agree. But be careful, because if she met a feminine noun and you want to specify this, you could also say
Elle l'a rencontrée
Meaning 'she met her', in which case you have to agree the ending. Because the "l'" is a complément objet direct (COD) placed before the verbal phrase, and if there is a COD before avoir used as an auxiliary you have to agree the verb with it. Similarly « Elle les a rencontrées » if she met a group of feminine things.