How to Draw Perpendicular and Parallel Lines

Euclid first put forth the definitions of parallel and perpendicular lines in his book Elements, the oldest math book in existence. Webster's Dictionary defines parallel as equidistant at all points never converging or diverging. In other words, parallel lines never meet. Perpendicular lines are lines that meet at right angles. Right angels are 90-degree angles.

Things You'll Need

• Compass, the kind used to draw circles
• Ruler or straight edge
• Paper

Instructions

Drawing Parallel Lines

1. In the middle of a piece of paper draw two dots.

2. Take the ruler and draw a straight line connecting the dots.

3. Open the compass to the distance that you want the second line to be from the first line.

4. Place the point of the compass on the first dot and draw a circle around the dot.

5. Pick up the compass. Do not change how wide open it is. Place the point of the compass on the second dot and draw a circle around it.

6. Take the ruler and draw a straight line connecting the very top of each circle. You now have two parallel lines. If you want a third parallel line, do the same at the very bottom point of the circles.

Drawing Perpendicular Lines

1. Draw a straight line in the middle of a piece of paper.

2. Put a dot in the middle of the line.

3. Open the compass. Put the point of the compass on the dot.

4. Draw a circle around the dot.

5. Where the circle crosses the line, draw another dot. The circle will cross the line in two spots. Label the the dots a and b.

6. Open the compass a little wider than the first circle. Place the point of the compass on dot a. Draw a circle around dot a. Then draw a circle around dot b by placing the compass point on dot b.

7. Where the circles cross each other, draw a dot. You will have two dots: one above the line and one below the line. Call these dots c and d.

8. Draw a straight line connecting c and d going through the first dot.

Tips & Warnings

• Square graph paper has parallel and perpendicular lines on it.

• Make sure that perpendicular lines are square. And parallel lines are equidistant.

References

• Singer, David, Geometry Plane and Fancy, 1998
• Clemens,C. Herbert, Clemens, Michael, Geometry in the Classroom, 1997 ,constructing perpendiculars p 130
• Euclid, The First six books of the Elements of Euclid, Annotations by Casey, John, 1885

Resources

• Math Open Reference Perpendicular Lines
• Math Open Reference Paraellel Lines
• Free Graph Paper