# Construction: Parallel Line

How to construct a line that is parallel to the given line: by using a compass and a straightedge (ruler).

## Example

### Given

Let's see how to construct a line

that is parallel to the given line

and that passes through

the given point not on the line.

### Solution

Draw a line

that passes through

the given line and the given point.

Place the point of the compass

at the intersection of the lines.

(blue point)

Draw an arc

that passes through the lines.

Without changing the radius of the compass,

place the point of the compass

at the given point.

Draw an arc (blue arc)

just like the previous arc.

Place the point of the compass

at the intersection

of the gray line and the previous arc.

(blue point)

The radius is the distance

from the blue point

to the intersecting point (blue arrow)

of the given line and the blue arc.

(blue dashed arc)

Without changing the radius of the compass,

place the point of the compass

at the intersection

of the gray line and the upper arc.

(blue point)

Draw an arc

that passes through the upper arc.

(blue arc)

Draw a line

that passes through

the given point and the intersection of the arcs.

Then the blue line is parallel to the given line.