straightedges

A straightedge is a tool consisting of a rigid, straight edge used to draw straight lines. It is typically unmarked, meaning it lacks measurement graduations like a ruler. In geometry and technical drawing, a straightedge serves to connect points, extend lines, and establish straight reference lines without providing length information.

In classical Euclidean geometry, the straightedge is used together with a compass to perform constructions. The straightedge can draw a line through two given points or the intersection of two previously drawn lines, but it cannot by itself determine a length. An ideal straightedge is modeled as an infinitely long, perfectly rigid, perfectly straight segment.

Drafting practice distinguishes between a straightedge and a ruler. A straightedge is unmarked, while a ruler may carry measurement marks. In architectural and engineering work, straightedges are used alongside set squares, T-squares, and other instruments to lay out lines, perpendiculars, and parallels without measuring distances.

Mathematically, the straightedge is one of the two classical tools in geometric construction, with the compass. Several results concern constructions with restricted tools: the Mohr–Mascheroni theorem shows compass-only constructions are possible, given a circle and its center, while the Poncelet–Steiner theorem shows that straightedge-only constructions are possible given a single circle with its center.

Historically, straightedges date to ancient Greek geometry, where they were used to draw lines and study properties of figures. The concept remains central in geometry education and in drafting, where it supports precise alignment and line work.