This example shows how to construct a line perpendicular to another line using a compass and straight edge.
Start by drawing a point where the perpendicular line will intersect.
Draw two points of equal distance away from the initial point along the line. The easiest way to do this is to draw a circle at the initial point and draw two points where the circle intersects the line.
Draw an arc upwards with a radius equal to the distance between the two outer points.
Repeat this process for the other point and mark where the two arcs intersect.
Draw a line from the point of intersection to the initial point.
We have finished constructing a perpendicular line.