The past participle: forms and agreement

You can hear the agreement with participles in -is, -it, -ert: la lettre que j'ai écrite (the letter I wrote), la porte est ouverte (the door is open), elle est morte (she died).

The agreement rules:

1. With être: agrees with the subject. Nous sommes arrivés. (We arrived.) Elles sont venues. (They came.)
2. With avoir: no agreement with the subject. Agreement with the direct object only if it comes before (le, la, les, que, quelle…): J'ai acheté des fleurs (no agreement: I bought flowers). Les fleurs que j'ai achetées (the flowers I bought). Je les ai achetées. (I bought them.) Quelle robe as-tu choisie ? (Which dress did you choose?)
3. With en, no agreement: Des pommes ? J'en ai mangé. (Apples? I ate some.)
4. Reflexive verbs: agreement with the subject if se is the direct object: Elle s'est lavée. (She washed.) No agreement if se is indirect (se + à) or if another direct object follows: Elle s'est lavé les mains. (She washed her hands.) Ils se sont parlé. (They talked to each other.) Ils se sont téléphoné. (They phoned each other.)
5. fait + infinitive never agrees: Elle s'est fait couper les cheveux. (She had her hair cut.)

Why? The rule with avoir comes from old French: when the participle comes after the object, you already know if it is feminine or plural, so it agrees.

Verbs with être that take avoir when they have a direct object: sortir, monter, descendre, rentrer, retourner, passer. Il est sorti. (He went out.) Il a sorti la poubelle. (He took the bin out.) Elle est montée. (She went up.) Elle a monté les valises. (She carried the suitcases up.)