How the use correctly the agreement of the past participle in passé composé?

Agreement of gender and number is necessary in two cases:The auxiliary verb used is être (in case of reflexives verbs and verbs related to movement, such as aller, venir, monter, descendre, etc.). In this case the verb has to be in agreement with the gender and number of the subject. For masculine singular no agreement in required. Masculine plural needs a 's', feminine singular an 'e' and feminine plural needs 'es' added to the end of the past participle. When the base forms end in 's', 'e' or 'es' respectively, no change is needed. Examples: Ils sont venus - They(masc.) came. Elle est venue - She came. Vous êtes venues - You(fem.) came.When the auxiliary verb is avoir but the object precedes the verb. In this case the past participle has to be in agreement with the object instead of the subject. This might happen when we use objective pronouns in french or in a subordinate sentence introduced by que. The procedure is the same as in case 1. Examples: J'ai acheté les chaussures -> Je les ai achetées. - I bought the shoes -> I bought them. J'aime les livres que tu as achetés. - I like the books that you bought.