An edge is an area of a 3D figure where two faces meet to form a line segment.
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Actually it really is called an edge!
A ruler has markings, a straight edge does not. In "straight edge and compass" constructions, you are not allowed to mark the straight edge. Things that are impossible using only a straight edge and compass are possible if markings are allowed (for example, it's possible to trisect an angle using a marked straight edge).
A perpendicular edge is a side of a plane shape that is at right angles (90 degrees) to another edge.
The line round the edge of the circle.