What evidence can I use to show the similarities between Socials and Greasers in The Outsiders?
That's an interesting question. At first glace the two groups are nothing alike. That's for sure what Ponyboy Curtis thinks. It's Cherry Valence who first makes him consider otherwise when she says the following in chapter 2.
"We have troubles you've never even heard of. You want to know something?" She looked me straight in the eye. "Things are rough all over."
I'm not sure how many body paragraphs you plan to write or how many similarities you need, but I think you could do a paragraph about surface level similarities and another one on "deeper" similarities.
On the surface, both groups are the same age. They are both mainly comprised of males. I'm not 100% sold on calling Cherry a Soc either, so you might want to argue that they are all males. Both groups attend the same school. Both groups enjoy going to the drive in. Both groups seem to enjoy a good rumble.
On the "deeper" level, it seems that both groups share an appreciation for beauty. That sounds weird in relation to two gangs that like fighting, but the sunset thing is a consistent motif throughout the novel.
"I pictured that, or tried to. Maybe Cherry stood still and watched the sun set while she was supposed to be taking the garbage out. Stood there and watched and forgot everything else until her big brother screamed at her to hurry up. I shook my head. It seemed funny to me that the sunset she saw from her patio and the one I saw from the back steps was the same one. Maybe the two different worlds we lived in weren't so different. We saw the same sunset."
Both groups believe that they are rebels of a sort, and both groups tend to internalize at home family issues. Lastly, because both groups gravitate toward rumbles so much, it's clear that their preferred method of dealing with emotional angst is to use violence.