Definitions:
a flat surface on which a straight line joining any two points on it would wholly lie

a level of existence, thought, or development

completely level or flat

(of a bird or an airborne object) soar without moving the wings; glide

an aeroplane

travel in an aeroplane

a tool consisting of a block with a projecting steel blade, used to smooth a wooden or other surface by paring shavings from it.

smooth (wood or other material) with a plane

a tall spreading tree of the northern hemisphere, with maple-like leaves and bark that peels in uneven patches.