Editing Straightedge (section)

==Compass-and-straightedge construction==
{{Main|Compass and straightedge}}

An idealized straightedge is used in [[compass-and-straightedge construction]]s in [[Euclidean geometry|plane geometry]].

It may be used:
* Given two points, to draw the line connecting them
* Given a point and a circle, to draw either tangent
* Given two circles, to draw any of their common tangents
* Or any of the other numerous geometric constructions

The idealized straightedge is:
* Infinitely long
* Infinitesimally thin (i.e. point width)
* Always assumed to be without graduations or marks, or the ability to mark
* Able to be aligned to two points with infinite precision to draw a line through them

It may not be marked or used together with the [[Compass (drafting)|compass]] so as to transfer the length of one segment to another.

It is possible to [[Mohr-Mascheroni theorem|do all compass and straightedge constructions without the straightedge]]. That is, it is possible, using only a compass, to find the intersection of two lines given two points on each, and to find the tangent points to circles. It is not, however, possible to do all constructions using only a straightedge. It ''is'' possible to [[Poncelet–Steiner theorem|do them with straightedge alone given a circle and its center]].