A mirror with a flat surface - planar
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Its base is a flat surface
A flat surface generally refers to a horizontal surface and is referred to as the plane.
A flat surface is no more that a plain horizontal surface with no depth. For example the surface of a table top is a flat surface, that is the surface only, not the depth of the top or the rest of the table
A flat surface that extends forever is a plane
Three points define a plane, which is a flat surface.