Headgear rhymes with:
acyclovir, atmosphere, azmeer, belvidere, benazir, biosphere, chemclear, ellesmere, fryrear, hemisphere, kinnear, lanphear, lanphere, lechmere, lincolnshire, ljubomir, maiziere, mcateer, meyerbeer, midyear, minniear, mountaineer, mystere, nyerere, petrolear, reindeer, retrovir, stratosphere, telesphere, vandermeer, vanderveer, vandeveer, whiteneir, windmere, yesteryear
Headgear sounds like:
hatcher, hatchery, hedger, hediger, heidecker, hetzer, hitchhiker, howitzer, hudsucker