Definition:Transversal (Geometry)

This page is about transversal in the context of geometry. For other uses, see transversal.

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 the context of geometry is also known as a traverse.

Also see

• Equal Alternate Angles implies Parallel Lines
• Equal Corresponding Angles or Supplementary Interior Angles implies Parallel Lines
• Parallelism implies Equal Alternate Angles, Corresponding Angles, and Supplementary Interior Angles

• Parallel Transversal Theorem

• Results about transversals in the context of geometry can be found here.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): transversal: 1.
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): transversal
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): transversal
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): transversal