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
We create a circle where the
of the desired right angle is a point on a circle. Thales Theorem says that any
diameter of a circle
a right angle to any point on the circle.
Printable step-by-step instructions
The 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 method
This is actually the same construction as Constructing a perpendicular at the endpoint of a ray.
Another way to do it is to
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.
||The line segment BC is a diameter of the circle center D
||BC is a straight line through the center.
||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.
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
Circles, Arcs and Ellipses
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