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Constructing a 90° angle
Geometry construction using a compass and straightedge
On this page we show how to construct (draw) a 90 degree angle with compass and straightedge or ruler. There are various ways to do this, but in this construction we use a property of Thales Theorem. We create a circle where the vertex of the desired right angle is a point on a circle. Thales Theorem says that any diameter of a circle subtends a right angle to any point on the circle. Printable step-by-step instructionsThe above animation is available as a printable step-by-step instruction sheet, which can be used for making handouts or when a computer is not available. Explanation of methodThis is actually the same construction as Constructing a perpendicular at the endpoint of a ray. Another way to do it is to
ProofThis construction works by using Thales theorem. It creates a circle where the apex of the desired right angle is a point on a circle. The image below is the final drawing above with the red items added. 
- Q.E.D Try it yourselfClick here for a printable worksheet containing two problems to try. When you get to the page, use the browser print command to print as many as you wish. The printed output is not copyright.Constructions pages on this siteLines
Angles
Triangles
Triangle CentersCircles, Arcs and Ellipses
PolygonsNon-Euclidean constructions
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