To illustrate that fact LiveScience has put up a gallery of pictures of some of the ancient forerunners of birds. There was a time during my memory when the only avian dinosaur ancestor that was widely known and acknowledged was Archaeopteryx.
Artist's rendering of Archaeopteryx.
Not any longer. They are a dime a dozen these days. Click on the link above and take a look at the gallery, and then compare what you've seen to those feathered creatures in your own backyard. I'm betting you'll be able to see the relationship.