A set square or triangle (

American English American English, sometimes called United States English or U.S. English, is the set of varieties of the English language native to the United States. English is the most widely spoken language in the United States and in most circumstances ...

) 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. T ...

, 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 degrees or radians corresponding to a quarter turn. If a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles. T ...

or other particular planar angle to a baseline. The simplest form of set square is a triangular piece of transparent

plastic Plastics are a wide range of synthetic or semi-synthetic materials that use polymers as a main ingredient. Their plasticity makes it possible for plastics to be moulded, extruded or pressed into solid objects of various shapes. This adaptabi ...

(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, line gauge, or scale, is a device used in geometry and technical drawing, as well as the engineering and construction industries, to measure distances or draw straight lines. Variants Rulers have long ...

and a half circle

protractor A protractor is a measuring instrument, typically made of transparent plastic or glass, for measuring angles. Some protractors are simple half-discs or full circles. More advanced protractors, such as the bevel protractor, have one or two sw ...

. The outer edges are typically bevelled. These set squares come in two usual forms, both

right triangle A right triangle (American English) or right-angled triangle (British), or more formally an orthogonal triangle, formerly called a rectangled triangle ( grc, ὀρθόσγωνία, lit=upright angle), is a triangle in which one angle is a right an ...

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 longest side of a right-angled triangle, the side opposite the right angle. The length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equ ...

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

s and

compasses A compass, more accurately known as a pair of compasses, is a technical drawing instrument that can be used for inscribing circles or arcs. As dividers, it can also be used as a tool to mark out distances, in particular, on maps. Compasses c ...

. 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: all other ...

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 A middle school (also known as intermediate school, junior high school, junior secondary school, or lower secondary school) is an educational stage which exists in some countries, providing education between primary school and secondary school. ...

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-Austrian 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 to the electromagnetic spectrum, measured by the metre and its derived scales. The microwave is between 1 meter to 1 millimeter. The millimetre (American and British English spelling differences#-re, -er, ...

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 image of a three-dimensional object. The term "axonometry" means "to measure along axes", and indicates that the dimensions and scaling of the coordin ...

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 movement of a craft or vehicle from one place to another.Bowditch, 2003:799. The field of navigation includes four general categories: land navigation, ...

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.

Navigation protractor triangles

See also

References

See also