# 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:

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**.

## 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

## 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**