# Definition:Transversal (Geometry)

## Definition

A transversal of two straight lines lying in the same plane is a straight line which intersects them in two different points.

The transversal is said to cut the two lines that it crosses. In the above diagram, $EF$ is a transversal of the lines $AB$ and $CD$.

It is also apparent that:

$AB$ is a transversal of the lines $EF$ and $CD$
$CD$ is a transversal of the lines $EF$ and $AB$

although this is not as obvious.

### Interior Angle

An interior angle of a transversal is an angle which is between the two lines cut by that transversal.

In the above figure, the interior angles with respect to the transversal $EF$ are:

$\angle AHJ$
$\angle CJH$
$\angle BHJ$
$\angle DJH$

### Exterior Angle

An exterior angle of a transversal is an angle which is not between the two lines cut by a transversal.

In the above figure, the exterior angles with respect to the transversal $EF$ are:

$\angle AHE$
$\angle CJF$
$\angle BHE$
$\angle DJF$

### Alternate Angles

Alternate angles are interior angles of a transversal which are on opposite sides and different lines.

In the above figure, the pairs of alternate angles with respect to the transversal $EF$ are:

$\angle AHJ$ and $\angle DJH$
$\angle CJH$ and $\angle BHJ$

### Corresponding Angles

Corresponding angles are the angles in equivalent positions on the two lines cut by a transversal with respect to that transversal.

In the above figure, the corresponding angles with respect to the transversal $EF$ are:

$\angle AHJ$ and $\angle CJF$
$\angle AHE$ and $\angle CJH$
$\angle BHE$ and $\angle DJH$
$\angle BHJ$ and $\angle DJF$

## Also known as

A transversal in this context is also known as a traverse.