Can I put a zebra dan with my betta fish?

I have a 10 gal tank and I have two tetras, a betta, and I am going to petco tomorrow to get 3 more tetras so they can school together. Would a zebra dan be compatible with my tank? I have a heater and everything and everything is up and running smoothly so far. my betta and the two tetras dont even aknoledge each other which i thought was wierd because i heard how the betta may kill the tetra and eat them or the tetras will bite the bettas fins but none of that has happened.