Which structure of the trachea prevents it from collapsing inward and obstructing the air passageway?

Answer: hyaline cartilage rings

Hyaline cartilage rings in a shape of a C prevent the tracheal wall from collapsing inward and obstructing airway (during inhalation). Posteriorly (open portion of each ring) there is not cartilage but there is muscle so that the esophagus can stretch (the esophagus is behind the trachea).