Is he a cheat?

I found out that my ex boyfriend was snapchatting a girl for a month and had a streak and changed her name to his friends name so I wouldn't find out and was sending her photos of him flexing and stuff. He also on a couple occasions asked her to met up with him at places with him and his friend, but the girl said no go out with your girlfriend. He lied to me and told me that he didn't talk to other girls at all and I thought he was the most loyal guy I ever knew and so did all our friends because they were jealous that I found such a great guy. He admitted to doing all of it after he broke up with me and I found out a couple days later from other people but said that he wouldn't call it cheating because he didn't physical do anything with her. He says and if it is I have cheated on him too because I have messaged guys... I asked one of my guy friends about homework a couple times. Would you consider this cheating?
I feel cheated on and lied to. 
Even though he didn't do anything with her he still tried
The month this was happening was while we were together and he broke up with me 3 days ago and tomorrow we are going to talk though it so we can move on. Just want to make sure I can use cheating as the word to describe what he did