If the family of the girl and the family of the boy know that they both want to marry, is this considered an engagement? What are the conditions of an engagement?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

An engagement means the proposal of a man to a woman for marriage, so if the guardian and the woman agree, then the engagement has taken place between them. This implies that it is not permissible for another person to ask her for marriage if he knows that another man has already asked her for marriage. The evidence is that the Prophet said: "One should not ask a woman for marriage if his brother (i.e. in faith) had already proposed to her.” [Muslim]

As regards the knowledge of the family of the girl and the family of the boy that they both want to marry, then this is not considered an engagement. For more benefit about an engagement and its etiquettes, please refer to Fatwa 88135.

Allaah Knows best.