When does the past participal of a reciprocal verb agree with its subject

Question

In a basic French grammar book one finds:

When reciprocal verbs take a direct object, the past participle agrees with the subject.
Ils se sont rencontrés à Venise.
Ils se sont embrassés.
Ils se sont mariés en mars.

However, by the book's own definition of an indirect object, i.e., one that inter alia follows a preposition, none of the verbs in those sentences are followed by a direct object and hence the part participles should not agree with their subject. 'Venise' is an indirect object since it follows à. In the second sentence the verb is intransitive and in the third sentence 'Mars' follows 'en' and hence is not a direct object. So I'm not understanding why the past participles in the above sentences agree with their subjects.

Answer 1

The reflexive pronoun is also an object. Whether it's direct or indirect depends on the verb.

Elles se sont rencontrées.

Because you rencontrer quelqu'un, COD.

Elles se sont parlé.

Because you parler à quelqu'un, COI.

Now, to be more precise, the participles aren't agreeing with their subjects, but their objects, which happen to be identical with the subject in reflexive verbs. Compare:

Elles se sont lavées.

Because you laver quelque chose, COD.

Elles se sont lavé les mains.

Because what they're washing is their hands, not themselves, and this direct object follows the verb. (Agreement only takes place if the relevant substantive precedes the verb.)

Here by the way is a flowchart of all the agreement rules on participles that I give to my more advanced students :)

Bare flowchart / with examples

P.S. French natives, even recipients of the Grand Prix de Poésie de l'Académie Française, sometimes make mistakes on this count!