The airline transport pilot reported that, while on downwind in the traffic pattern, he lowered the landing gear handle and verbally announced “gear down.” He looked at the cockpit indications to verify the landing gear was down and locked; however, he then shifted his attention outside of the cockpit to visually scan for three aircraft approaching and entering the traffic pattern. He reported that he did not confirm the landing gear was down and locked, as he was distracted with scanning for the other traffic. During landing, the bottom of the fuselage sustained substantial damage. A postaccident functional test of the landing gear revealed no mechanical anomalies with the landing gear system. The pilot reported there were no preimpact mechanical malfunctions or failures with the airframe and engines that would have precluded normal operation.