Constructing a parallel through a point
(angle copy method)

Geometry construction using a compass and straightedge

This page shows how to construct a line
parallel
to a given line that passes through a given point with compass and straightedge or ruler.
It is called the 'angle copy method' because it works by using the fact that a
transverse line
drawn across two parallel lines creates pairs of equal
corresponding angles.
It uses this in reverse - by creating two equal corresponding angles, it can create the parallel lines.

This construction works by using the fact that a
transverse line
drawn across two parallel lines creates pairs of equal
corresponding angles.
It uses this in reverse - by creating two equal corresponding angles, it can create the parallel lines.

The image below is the final drawing above with the red items added.