Rook+King vs. King Mate

Today, I was playing a game on live chess. Our ratings were very similar. Although my rating was higher, he was a better player. He used many tactics on me to get the upper hand. During the endgame, he had a rook and a king when I only had a king left. He could have easily won, had he known the process of getting a rook and king vs. king mate. Here is what happened in the game. It became a draw on time.

I, when we played this game, knew how to get a rook and king vs. king checkmate, and was not sure if he did. For the people who do not know how to get this type a checkmate, she the diagram below.

There are also more advanced ways for this type of checkmate, but it varies on the position, so I won't get into details. I hope you guys have learned something. Please comment and tell me if there are any mistakes that I didn't find. Hope to play you on live chess! (And see that you know this.)

 

Edit: I knew that their were faster ways, but I showed the most consistent way for beginners. :)