View source for Set square

{{Short description|Object used in engineering and technical drawing}}
{{for|the British business incubator network|SETsquared}}
{{use dmy dates|date=July 2021|cs1-dates=y}}
[[Image:Reglas.svg|thumb|250px|triangle, set square]]

A '''set square''' or '''triangle''' ([[American English]]) is an object used in engineering and [[technical drawing]], with the aim of providing a [[straightedge]] at a [[right angle]] or other particular planar angle to a [[:wikt:baseline|baseline]].

== Types ==
The simplest form of set square is a triangular piece of transparent [[plastic]] (or formerly of polished wood) with the centre removed. More commonly the set square bears the markings of a [[ruler]] and a half circle [[protractor]]. The outer edges are typically [[bevel]]led.  These set squares come in two usual forms, both [[right triangle]]s: one with 90-45-45 degree angles, the other with 30-60-90 degree angles.  Combining the two forms by placing the [[hypotenuse]]s together will also yield 15° and 75° angles.  They are often purchased in packs with [[protractor]]s and [[Compass (drafting)|compasses]].

Less commonly found is the adjustable set square.  Here, the body of the object is cut in half and rejoined with a [[hinge]] marked with angles.  Adjustment to the marked angle will produce any desired angle up to a maximum of 180°.

== {{lang|de|Geodreieck}} ==
[[Image:Set square Geodreieck.svg|thumb|250px|Original {{lang|de|Geodreieck}}]]
[[Image:GeoDreieck-Ingen-Proj-Mark.jpg|thumb|250px|Variant of larger {{lang|de|TZ-Dreieck}} with extra markings]]

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.<ref name="Vollrath_1999"/><ref name="Vollrath_2006"/><ref name="Willner_2021"/> Being a mandatory tool used by pupils in [[middle school]] and higher in German-speaking and neighbouring countries, this specific design is named "{{lang|de|{{ill|Geodreieck|de}}}}" (short form of "{{lang|de|Geometrie-Dreieck}}", meaning "geometry triangle") or similar.<!-- f.e. Germany&Austria: Geodreieck, Netherlands: Geodriehoek, Luxembourg: Geodräieck, Slovenia: Geotrikótnik, France: Équerre aristo --><ref name="Willner_2021"/> It was originally developed<!-- and trademarked by ARISTO Graphic Systeme GmbH & Co. KG up to 1987-01-12 (per DPMA) and now as R337 300 by GEOtec Zeichen- und Kunststofftechnik GmbH (per WIPO) --> in 1964 by the German manufacturer {{ill|Dennert &amp; Pape Aristo-Werke|de}} (after several refirmations now ''Geotec Schul- und Bürowaren GmbH'').<ref name="Aristo_2013"/><ref name="Bergmayr_2019"/><ref name="Praxmarer_2019"/><ref name="Willner_2021"/><ref name="Hrdina_2021"/> 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&nbsp;cm and features a 2×7&nbsp;cm symmetry scale in [[millimeter]] and [[degree (angle)|degree]] raster.<ref name="Willner_2021"/> 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 projection|dimetric]] [[axonometry]] per ISO&nbsp;5456-3,<ref name="Walz_2017"/> others feature angle scales in [[gon (unit)|gon]]s instead of degrees. Several other somewhat similar designs named "{{lang|de|TZ-Dreieck}}" ("TZ triangle") exist for (larger) technical drawings (TZ from German: {{lang|de|Technisches Zeichnen}}). The scale reaches from 10 to 10 cm, or even 11 to 11 cm.

== Navigation protractor triangles ==
<!-- Section header used in incoming redirects to this article -->
<!-- This subtopic could probably become an article on its own, but needs more research -->
Similar to the {{lang|de|Geodreieck}}, a number of other protractor triangle types exist for [[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.
{{SeeAlso|:de:Kursdreieck|:de:Anlegedreieck|:de:Kartenbesteck}}<!-- to be reworked into links in English WP as soon as we have entries for them as well -->

== See also ==
* [[Speed square]]
* [[Technical drawing tool]]

== References ==
{{Reflist|refs=
<ref name="Aristo_2013">{{cite web |title=Unternehmen / Geschichte |language=de |publisher=GEOtec Zeichen- und Kunststofftechnik GmbH |date=2013 |url=http://www.aristo.at/go/unternehmen |access-date=2015-08-28 |url-status=live |archive-url=https://web.archive.org/web/20210711121831/https://www.aristo.at/unternehmen/ |archive-date=2021-07-11 |quote=[…] 1964 […] Das klassische Geodreieck wird entwickelt und als international registrierte und geschützte Marke eingetragen. Inzwischen millionenfach gefertigt und in vielen Ländern zum Standard-Zeichengerät in der Schule und Ausbildung avanciert […]}}</ref>
<ref name="Bergmayr_2019">{{cite news |author-first=Thomas |author-last=Bergmayr |title=Das Geodreieck kommt aus Tirol |language=de-AT |newspaper=[[Der Standard]] |number=Journal 9291 |date=2019-09-11 |page=15}}</ref>
<ref name="Vollrath_1999">{{cite book |title=80. Historische Winkelmeßgeräte in Projekten des Mathematikunterrichts |chapter=1. Das Geodreieck und seine Vorfahren |language=de |series=Der Mathematikunterricht |volume=45 |issue=4 |date=1999 |pages=42–58 [3–10] |author-first=Hans-Joachim |author-link=:de:Hans-Joachim Vollrath |author-last=Vollrath |url=http://www.history.didaktik.mathematik.uni-wuerzburg.de/vollrath/papers/080.pdf |access-date=2017-11-07 |url-status=dead |archive-url=https://web.archive.org/web/20171107164846/http://www.history.didaktik.mathematik.uni-wuerzburg.de/vollrath/papers/080.pdf |archive-date=2017-11-07}} (29 pages)</ref>
<ref name="Vollrath_2006">{{cite web |title=Das Geometrie-Dreieck |language=de |author-first=Hans-Joachim |author-link=:de:Hans-Joachim Vollrath |author-last=Vollrath |date=2006 |publisher=Institut für Mathematik, [[Universität Würzburg]] |url=https://www.didaktik.mathematik.uni-wuerzburg.de/history/ausstell/winkelmesser/geodreieck.html |access-date=2021-07-11 |url-status=live |archive-url=https://web.archive.org/web/20090405190310/http://www.didaktik.mathematik.uni-wuerzburg.de/history/ausstell/winkelmesser/geodreieck.html |archive-date=2009-04-05}}</ref>
<ref name="Walz_2017">{{cite book |title=Lexikon der Mathematik |language=de |chapter=Geodreieck |author-first=Guido |author-last=Walz |edition=2 |date=2017 |orig-date=2016-11-18 |volume=2: Eig bis Inn |publisher=[[Springer Spektrum]] / [[Springer Verlag GmbH]] |isbn=978-3-66253503-5 |url=https://www.spektrum.de/lexikon/mathematik/geodreieck/3442 |access-date=2021-07-12 |url-status=live |archive-url=https://web.archive.org/web/20210712111202/https://www.spektrum.de/lexikon/mathematik/geodreieck/3442 |archive-date=2021-07-12}}</ref>
<ref name="Praxmarer_2019">{{cite web |title=Das Geodreieck – das Original aus Wörgl |language=de-AT |author-first=Christoph |author-last=Praxmarer |department=Wirtschaft |date=2019-09-09 |publisher=[[Österreichischer Rundfunk]] (ORF) |website=tirol.orf.at |url=https://tirol.orf.at/stories/3010465/ |access-date=2021-07-12 |url-status=live |archive-url=https://web.archive.org/web/20210712111603/https://tirol.orf.at/stories/3010465/ |archive-date=2021-07-12}}</ref>
<ref name="Willner_2021">{{cite news |title=Mittelständler Aristo: Dieses Unternehmen hat das Geodreieck erfunden |language=de |department=Wirtschaft |author-first=Johannes |author-last=Willner |date=2021-03-14 |newspaper=[[Frankfurter Allgemeine Zeitung]] (FAZ) |publication-place=Frankfurt am Main, Germany |location=Gießen, Germany |url=https://www.faz.net/aktuell/wirtschaft/unternehmen/geodreieck-das-mittelstaendische-unternehmen-aristo-hat-es-erfunden-17225868.html |access-date=2021-07-12 |url-status=live |archive-url=https://web.archive.org/web/20210519191540/https://www.faz.net/aktuell/wirtschaft/unternehmen/geodreieck-das-mittelstaendische-unternehmen-aristo-hat-es-erfunden-17225868.html |archive-date=2021-05-19}}</ref>
<ref name="Hrdina_2021">{{cite web |title=Firma Geotec plant Neustart |language=de-AT |date=2021-04-04 |author-last=Hrdina |author-first=Jasmine |website=top.tirol |publisher=Target Group Publishing GmbH |publication-place=Innsbruck, Austria |url=https://www.top.tirol/wirtschaftsmeldungen/wirtschaftsnews/firma-geotec-plant-neustart |access-date=2021-07-12 |url-status=live |archive-url=https://web.archive.org/web/20210712112529/https://www.top.tirol/wirtschaftsmeldungen/wirtschaftsnews/firma-geotec-plant-neustart |archive-date=2021-07-12}}</ref>
}}

{{commons category|Set squares}}

{{Measuring and alignment tools}}{{Authority control}}

[[Category:Technical drawing tools]]
[[Category:Hand tools]]
[[Category:Squares (tool)]]