Constructing a perpendicular at the end of a ray with compass and straightedge

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Constructing a perpendicular at the endpoint of a ray

Click here for a printable worksheet

This demonstration shows how to draw a perpendicular at the endpoint of a ray or line segment, using only a compass and straightedge. See "Introduction to Euclidean Constructions". We start with a ray. The result is a vertical line perpendicular to the ray at its endpoint.

Instructions Click on 'Next' to go through the construction one step at a time, or click on 'Run' to let it run without stopping.

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Step-by-step Instructions

Step 1	Pick a point not on the line, about 6 cm from the endpoint of the ray. Its exact location is not important. Label it D.
Step 2	Set the compass on point D and set its width to the endpoint of the ray.
Step 3	Draw an arc that crosses the ray and extends over and above the ray endpoint. (If you prefer, draw a complete circle.)
Step 4	Draw a diameter through D from the point where the arc crosses the ray.
Step 5	Draw a line from the ray's endpoint to the endpoint of the diameter line
Step 6	Done. The last line drawn is perpendicular to the ray.

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

Lines

Angles

Triangles

Triangle Centers

Circles, Arcs and Ellipses

Non-Euclidean constructions