Constructing a 90° angle

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 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.

  Argument Reason
1 The line segment AB is a diameter of the circle center D AB is a straight line through the center.
2 Angle ACB has a measure of 90°. The diameter of a circle always subtends an angle of 90° to any point (C) 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.

Other constructions pages on this site




Right triangles

Triangle Centers

Circles, Arcs and Ellipses


Non-Euclidean constructions