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.

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.

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.