of the scene, the two lovers part ways and discover each other's identities, creating suspense and uncertainty. InAct III, Scene 5 Romeo and Juliet have consummated the love they discovered in Act I. They also part ways with uncertainty, Romeo banished to Mantua, and Juliet left at the hands of her father who will soon demand she marry Paris.

Both Act I, Scene 1, and Act III begin with a violent meeting between the Capulet and Montague families. In Act I, some low-level Capulets run into Benvolio and two other Montague men, and the Capulets purposely bait the Montagues into fighting. It's the same in Act III, when Tybalt and his cohorts go looking for Romeo so Tybalt can fight him. In both situations, Benvolio serves as a voice of reason and peace (which helps explain the "ben" root of his name, which means "good"), contrasting with Tybalt's sheer aggression and meanness (which helps to explain the similarity between his name and the word "tyrant").  In both cases, the prince intervenes and imposes punishments he hopes will prevent further violence in the community. In Act I, he makes Lords Montague and Capulet responsible for any further altercations between their families, and in Act III, he banishes Romeo after he murders Tybalt.

The above answers are correct in citing the main similarity between these two scenes is the fact that these are the two main scenes of physical fighting between the Capulets and the Montagues.

What makes these two scenes most parallel, in my opinion, is the way each fight starts.  Though the fight in Act 1 is begun by two servants, it starts with the exchange of petty insults.  The fight grows larger because members of each house, without thinking about the reason behind the conflict, join the fight to stand up for their respective families.

The fight scene in Act 3 is very much the same, except that this time, though Tybalt believes he is being insulted by Romeo's kindness, Romeo's intentions (for once) are pure.  Tybalt does not even recognize this because he has grown so accustomed to automatic scorn and hatred (both for and from) the Montagues that there is no reason for him to consider Romeo to be genuinely kind.

It was necessary for Shakespeare to include the first fight scene to set the tone for the second and to show the sort of hidden seriousness of the hatred between the families.  Both are started because one house feels insulted by the other.  Neither of the fights are justified which heightens the pettiness of the overall feud between these families.  Additionally, there is a bandwagon effect in both fights, which displays the sense of automatic (if irrational) loyalty by the characters to their respective sides.  Consider that Mercutio, who isn't even related to the Montagues, fights as if he is Romeo's brother.  Then, only when he is mortally wounded does he realize just how out of hand the hatred has become.  His famous line, "A plague on both your houses!" is the alarm that, at last, it has gone too far.

Though a dramatic comparison, it should be noted that entire wars have started as a result of one leader feeling insulted by someone.  Gang violence and warfare so prevalent in major US cities could likely be traced back to a series of once petty insults that escalated to full blown hatred.  In just two scenes, Shakespeare has captured several common human emotions, desires, and actions that result from what is often passed off as "petty insults."