The House Finchs are described by the Cornell Lab of Ornithology as "small-bodied finches with fairly large beaks and somewhat long, flat heads. The wings are short, making the tail seem long by comparison. Many finches have distinctly notched tails, but the House Finch has a relatively shallow notch in its tail." The image above shows the large beak and long flat head. The image below, caught in flight at Sabino Canyon in December of 2015, shows the short wings, seen in relation to the head, body and tail, as well as the red rump.
The image below shows the finch in flight, demonstrating a fixed-wing pause, with wings tucked in, a form of intermittent flight called flap-bounding. This strategy reduces the power required during fight. Flap-bounding offers saving in power during fast flight at maximum range speed or faster. Flap-gliding is an alternative form of intermittent flight with a gliding phase with wings fully extended, and is more efficient especially at slow or intermittent speeds. Reference: Lovette IJ and Fitzpatrick JW, The Cornell Lab of Ornithology Handbook of Bird Biiology, Third Edition, Wiley, pp. 161-162.
Below a male and a female mixing it up a bit.
All images captured at Sabino Canyon, December 2015.