How to construct (draw) a 90 degree angle with compass and straightedge or ruler

Constructing a 90° angle

Geometry construction using a compass and straightedge

- Printable problem worksheet
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Click on 'Next' to go through the construction one step at a time, or click on 'Run' to let it run without stopping. (If there is no image below, see support page.)

Step-by-step Instructions

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After doing this	Your work should look like this
Start with a ray with endpoint A. The right angle will have A as its vertex.
1. Pick a point not on the given line, about 6 cm from one of its endpoints. Its exact location is not important. Label it D.
2. Set the compass on point D and set its width to the chosen endpoint .
3. Draw an arc that crosses the given line and extends over and above the chosen endpoint. (If you prefer, draw a complete circle.)
4. Draw a diameter through D from the point where the arc crosses the given line.
5. Draw a line from the chosen endpoint to the endpoint of the diameter line
6. Done. The last line drawn is perpendicular to the given line.

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

Triangle Centers

Circles, Arcs and Ellipses

Non-Euclidean constructions