
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 stepbystep instructions
The above animation is available as a
printable stepbystep instruction sheet, which can be used for making handouts
or when a computer is not available.
Explanation of method
This is actually the same construction as Constructing a perpendicular at the endpoint of a ray.
Another way to do it is to
Proof
This 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.

Argument 
Reason 
1 
The line segment BC is a diameter of the circle center D 
BC is a straight line through the center. 
2 
Angle BAC has a measure of 90°. 
The diameter of a circle always subtends an angle of 90° to any point (A) on the circle.
See Thales theorem. 
 Q.E.D
Try it yourself
Click 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 site
Lines
Angles
Triangles
Right triangles
Triangle Centers
Circles, Arcs and Ellipses
Polygons
NonEuclidean constructions
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