The first similarity between the two shows is that both Rent and La Boheme are operas. When we think of operas and opera singers we usually imagine something like this:
The above link and picture are both from the opera La Boheme, which is what we would consider a "normal opera". I'm pretty sure I remember everyone in our class, teachers included, seeing Rent. (THANK YOU! You guys are the best!) I'm pretty sure you weren't sitting there during the show thinking "wow, what a great opera." However, it is important to remember the basic definition of an opera - an opera is a show in which everything is sung. If you remember from Rent, there were very few spoken words. The way that information was given to the audience and the way the characters conversed was through song. Rent is therefore considered a rock opera.
Much of the music from Rent is based off of La Boheme's music. There are a few themes, such as Musetta's Waltz, that are repeated throughout Rent's music. Below is a link to Musetta's Waltz:
And here is a link to Musetta's Waltz being played in the song La Vie Boheme from Rent (go to the time 6:45):
The characters in Rent are also directly based off of the characters in Puccini's La Boheme. Below are the character's names and hobbies in La Boheme next to their counterpart in Rent (La Boheme on the left, Rent on the right):
Marcello, a painter = Mark, a videographer (Videos "paint a picture" through image)
Rodolfo, a poet = Rodger, a songwriter (poetry = lyrics of song)
Mimí, a seamstress = Mimi, a dancer
Musetta, a singer = Maureen, a singer/performer
Schaunard, a musician = Angel Dumott Schaunard, a street performer/drummer
Colline, a philosopher = Collins, a computer aged philospher
Benoît, the landlord = Benny, the landlord
Finally, the plot in La Boheme and Rent are crazily similar. La Boheme is about a group of struggling artists living in the Latin Quarter of Paris in the 1830s, during the Tuberculosis crisis. Rent is about a group of struggling artists living in New York in the late 1900s, during the height of the AIDS crisis. In both of these shows, the artists are called "bohemians", which according to dictionary.com, is a person, as an artist or writer, who lives and acts free of regard for conventional rules and practices." In the interest of time, I'm not going to go through the whole plot of La Boheme versus Rent, but they are shockingly similar. Many of the same events occur in both shows. They are, of course, somewhat different, but Rent is very closely based off of La Boheme.