# Constructing a Parallel Line

How to construct a line that is parallel to the given line.

## Goal

Goal:

Constructing the line

that is parallel to the given line

and that passes through the given point

which is not on the line.

## How to Construct

Draw a line that passes through

the given line and the given point.

(red line)

Place the point of the compass

at the intersection of the lines.

(red point)

Draw an arc that passes through the lines.

(red arc)

Without changing the radius of the compass,

place the point of the compass

at the given point.

(red point)

Draw an arc (red arc)

just like the previous arc.

Place the point of the compass

at the intersection

of the blue line and the previous arc.

(red point)

The radius is the distance

from the red point

to the intersecting point

of the given line and the blue arc.

(red dashed arc)

Without changing the radius of the compass,

place the point of the compass

at the intersection

of the blue line and the upper arc.

(red point)

Draw an arc

that passes through the upper arc.

(red arc)

Draw a line that passes through

the given line and the intersection of the arcs.

(red line)

Then the red line is parallel to the given line.

## Why the Constructed Line is Parallel to the Given Line?

What you did is constructing congruent angles.

(red angles)

So the red angles are corresponding angles

which are congruent.

So the constructed line

is parallel to the the given line.