A set square or triangle (

American English American English, sometimes called United States English or U.S. English, is the set of variety (linguistics), varieties of the English language native to the United States. English is the Languages of the United States, most widely spoken lang ...

) is an object used in engineering and

technical drawing Technical drawing, drafting or drawing, is the act and discipline of composing drawings that visually communicate how something functions or is constructed. Technical drawing is essential for communicating ideas in industry and engineering. ...

, with the aim of providing a

straightedge A straightedge or straight edge is a tool used for drawing straight lines, or checking their straightness. If it has equally spaced markings along its length, it is usually called a ruler. Straightedges are used in the automotive service and ma ...

at a

right angle In geometry and trigonometry, a right angle is an angle of exactly 90 Degree (angle), degrees or radians corresponding to a quarter turn (geometry), turn. If a Line (mathematics)#Ray, ray is placed so that its endpoint is on a line and the ad ...

or other particular planar angle to a baseline.

Types

The simplest form of set square is a triangular piece of transparent

plastic Plastics are a wide range of synthetic polymers, synthetic or Semisynthesis, semisynthetic materials composed primarily of Polymer, polymers. Their defining characteristic, Plasticity (physics), plasticity, allows them to be Injection moulding ...

(or formerly of polished wood) with the centre removed. More commonly the set square bears the markings of a

ruler A ruler, sometimes called a rule, scale, line gauge, or metre/meter stick, is an instrument used to make length measurements, whereby a length is read from a series of markings called "rules" along an edge of the device. Usually, the instr ...

and a half circle

protractor A goniometer is an instrument that either measures an angle or allows an object to be rotated to a precise angular position. The term goniometry derives from two Greek words, γωνία (''gōnía'') 'angle' and μέτρον (''métron'') ' me ...

. The outer edges are typically

bevel A bevelled edge (UK) or beveled edge (US) is an edge of a structure that is not perpendicular to the faces of the piece. The words bevel and chamfer overlap in usage; in general usage, they are often interchanged, while in technical usage, they ...

led. These set squares come in two usual forms, both

right triangle A right triangle or right-angled triangle, sometimes called an orthogonal triangle or rectangular triangle, is a triangle in which two sides are perpendicular, forming a right angle ( turn or 90 degrees). The side opposite to the right angle i ...

s: one with 90-45-45 degree angles, the other with 30-60-90 degree angles. Combining the two forms by placing the

hypotenuse In geometry, a hypotenuse is the side of a right triangle opposite to the right angle. It is the longest side of any such triangle; the two other shorter sides of such a triangle are called '' catheti'' or ''legs''. Every rectangle can be divided ...

s together will also yield 15° and 75° angles. They are often purchased in packs with

s and compasses. Less commonly found is the adjustable set square. Here, the body of the object is cut in half and rejoined with a

hinge A hinge is a mechanical bearing that connects two solid objects, typically allowing only a limited angle of rotation between them. Two objects connected by an ideal hinge rotate relative to each other about a fixed axis of rotation, with all ...

marked with angles. Adjustment to the marked angle will produce any desired angle up to a maximum of 180°.

In some European countries a common form of set square combines a 90-45-45 triangle, a ruler and a protractor into a single tool made of stiff or slightly flexible transparent plastic. Being a mandatory tool used by pupils in

middle school Middle school, also known as intermediate school, junior high school, junior secondary school, or lower secondary school, is an educational stage between primary school and secondary school. Afghanistan In Afghanistan, middle school includes g ...

and higher in German-speaking and neighbouring countries, this specific design is named "" (short form of "", meaning "geometry triangle") or similar. It was originally developed in 1964 by the German manufacturer (after several refirmations now ''Geotec Schul- und Bürowaren GmbH''). Relatively uncommon in English-speaking countries, this is sometimes called a "protractor triangle", a term, however, also used for other similar designs. The original design has a hypotenuse length of 15.8 cm and features a 2×7 cm symmetry scale in

millimeter 330px, Different lengths as in respect of the electromagnetic spectrum, measured by the metre and its derived scales. The microwave is between 1 metre to 1 millimetre. The millimetre (American and British English spelling differences#-re, -er, i ...

and degree raster. Variants in larger sizes, with fixed or detachable handles, with or without bevelled edges (facets), and with or without ink nodules or embossed labels exist as well. Some variants have extra markings at angles of 7° and 42° (138° and 173°) in addition to the normal 45° and 90° markings to ease dimetric

axonometry Axonometry is a graphical procedure belonging to descriptive geometry that generates a Planar graph, planar image of a three-dimensional object. The term "axonometry" means "to measure along Cartesian coordinate system, axes", and indicates that ...

per ISO 5456-3, others feature angle scales in gons instead of degrees. Several other somewhat similar designs named "" ("TZ triangle") exist for (larger) technical drawings (TZ from German: ). The scale reaches from 10 to 10 cm, or even 11 to 11 cm.

Navigation protractor triangles

Similar to the , a number of other protractor triangle types exist for

navigation Navigation is a field of study that focuses on the process of monitoring and controlling the motion, movement of a craft or vehicle from one place to another.Bowditch, 2003:799. The field of navigation includes four general categories: land navig ...

purposes. Various designs are named navigation (protractor) triangle, nautical navigational triangle, nautical set square, Portland (navigational) triangle or Portland protractor triangle, Kent-type triangle, Inoue-type A/B nautical triangle or plotting triangle, course triangle, yachtsmen triangle, and supporting triangle. However, some widely used navigational protractors, such as the Cras protractor, are not triangles.

References

{{Authority control Technical drawing tools Hand tools Squares (tool)

Types

Navigation protractor triangles

See also

References