Final answer:
Small, non-cartilaginous airways in the lungs are called bronchioles. They rely on the elasticity of their walls and the presence of smooth muscle to stay open.
Step-by-step explanation:
Small, non-cartilaginous airways in the lungs are known as bronchioles. Unlike the larger bronchi, which have cartilage for support, bronchioles rely on the elasticity of their walls to stay open. As the passageways decrease in diameter, the relative amount of smooth muscle increases. Bronchioles are also innervated by nerves of both the parasympathetic and sympathetic nervous systems, controlling muscle contraction or relaxation in response to cues from the nervous system.