The Beggar's Opera Discussion

In Act II of The Beggar's Opera starting at Scene 11, we are introduced to the love triangle that exists between Macheath, Polly, and Lucy. As a satire, the play presents each of the female rivals in a particular, rather overblown fashion; yet they still present familiar sentiment. Throughout the course, we have been introduced to many other works featuring complicated romantic liaisons, from Fantomina to Eloisa to Abelard. It is from these works we have built up ideas about how the concept of love was portrayed in the period.

Since satire inevitably relies on previous knowledge to be amusing, in what way does the love triangle track with these ideas we have already conceived? In what way does it digress from them? How are they defied in order to create humor?