Les décorations ________ tu as achetées sont très belles.

Question

Hey, in this question I understand why the answer is "que," but why is "achetées" matching "les décorations" if it's preceded by "avoir" instead of "être"?

Accepted Answer

It is as Jim notes. A few links that cover the topic. 
Compound conjugations with avoir only have past participle agreement with the direct object, and only if it precedes the verb, as in the example sentence.
The 2nd link is an excellent, entertaining TEDX presentation on the potential to simplify French spelling and grammar. It is in French, but not too hard to follow, as the captions and visuals are helpful. At about 14 minutes in is a great demonstration of “why” direct object before the verb agrees, but not direct object after the verb. 
 
https://progress.lawlessfrench.com/revision/grammar/special-cases-when-the-past-participle-agrees-in-number-and-gender-when-used-with-avoir-in-le-passe-compose-conversational-past?
https://www.ted.com/talks/arnaud_hoedt_jerome_piron_la_faute_de_l_orthographe?language=fr

Answer

Hi Diego,Les décorations is the direct object of acheter but placed before the verb in this construction, therefore there is concordance between the direct object and the past participle achetées with avoir in this type of sentence structure.Hope this helps.Jim