First opened for the 1968 school year, Falcon Gymnasium is home to the volleyball, basketball and wrestling teams. In 2020, local car dealership Greenwood Chevrolet expanded their sponsorship to include naming the court to Greenwood Chevrolet Court. The original wooden bleachers were replaced with new plastic bleachers for the 2006 school year and has a capacity of 2,000 seats. New LED lights were installed in 2018. The court was sanded and repainted during the summer of 2022 to reflect the new branding.

Falcon Gymnasium and Greenwood Chevrolet Court have hosted thousands of games including OHSAA volleyball, basketball, and wrestling postseason contests. Additionally, Falcon Gymnasium has hosted Vice President Al Gore, campaign rallies for Hillary Clinton and John Kerry, charity basketball games involving the Cleveland Browns and Pittsburgh Steelers as well as a pro wrestling event.