How to Construct a Perpendicular Line Segment

The compass is essential for undertaking geometric constructions.

Constructing a perpendicular line segment is one of the basic operations in geometrical construction. Other basic operations include bisecting angles, dividing line segments and duplicating angles. With a thorough understanding of these and other fundamental techniques, you can apply them in conjunction to construct a wide variety of geometric forms. Besides having applications in drafting, the arts and on-site layout, the hands-on practice of constructing helps to develop problem-solving skills and a more thorough understanding of geometry.

Things You'll Need

• Ruler
• Compass

Instructions

1. Use a ruler to draw a horizontal line from side to side on a piece of paper. This is your reference line.

2. Mark an intersection point in the middle of the reference line where the perpendicular segment will pass through.

3. Spread your compass apart 2 inches from its point to the marking tip. Place the compass point on the intersection point and scribe a mark on your reference line on either side of the intersection point. Your reference line should now have three marks on it: the intersection point and two scribed marks 2 inches on either side of it.

4. Widen the spread of your compass to 4 inches and place the compass point on the first scribed point. Imagine where the perpendicular segment will pass on the paper and draw an arc so that it passes through the segment that you're imagining, both above and below your reference line.

5. Place the point of the compass on the second scribed point and draw a couple of arcs that intersect through the arcs that you just made. If you were unable to make an intersection, go back and make the arcs from Step 3 a little bigger. You should now have two points where your arcs intersected above and below the reference line.

6. Draw a line segment through where your arcs intersected. If done correctly, the line segment should also pass perpendicularly through the intersection point that you drew in Step 2.

Tips & Warnings

• The 2-inch and 4-inch spread of the compass is only recommended for introductory purposes. With practice, you will get a better feel for the settings necessary to give you the best accuracy for your application.

References

• Sonoma State University: Drop a Perpendicular