# Transversal

Pronunciation: /trænzˈvɜr səl/ Explain

 Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now) Manipulative 1: Transversal of two lines.

A transversal is a line that intersects two other possibly parallel lines. Transversal are important in geometry because the theorems based on the relationships of angles formed by a transversal are used in many other theorems. The line that intersects the two other lines is called the transversal. The lines that are crossed are called the transversed lines. The various pairs of angles in a transversal are named to make it easier to describe the relationships. Click on the check boxes in manipulative 1 to see which angles match which names.

 Figure 2: Transversal

Names of angles in a transversal
NameDescriptionAngle numbers
ExteriorExterior angles are on the outside of the transversed lines.Angles 3, 4, 5 and 6 are exterior angles.
InteriorInterior angles are between the transversed lines.Angles 1, 2, 7 and 8 are interior angles
AlternateAlternate angles are on opposite sides the transversal.Angles 1, 4, 5, and 8 are alternate to 2, 3, 6 and 7.
ConsecutiveConsecutive angles are adjacent angles on the same side of the transversal.Angle pairs 1 and 8, 2 and 7 are consecutive.
CorrespondingCorresponding angles are angles that are in the same positions relative to the two intersections.Angle pairs 1 and 5, 2 and 6, 3 and 7, 4 and 8 are corresponding angles.
VerticalVertical angles are opposite each other at an intersection.Angle pairs 1 and 3, 2 and 4, 5 and 7, 6 and 8 are vertical angles.
Alternate interiorAngle pairs that are interior angles and are opposite each other.Angle pairs 1 and 7, 2 and 8 are alternate interior angles.
Alternate exteriorAngle pairs that are exterior angles and are opposite each other.Angle pairs 3 and 5, 4 and 6 are alternate exterior angles.
Table 1: Names of angles in a transversal

### Postulates and Theorems

There are a number of postulates and theorems associated with transversals of parallel lines:
• Corresponding Angles Congruence Postulate: Corresponding angles of a transversal of parallel lines are congruent.
• Alternate Exterior Angles Congruence Theorem: Alternate exterior angles of a transversal of parallel lines are congruent.
• Alternate Interior Angles Congruence Theorem: Alternate interior angles of a transversal of parallel lines are congruent.
• Consecutive Interior Angles Supplement Theorem: Consecutive interior angles of a transversal of parallel lines are supplementary.
• Corresponding Angles Congruence Converse Theorem: If any pair of corresponding angles of a transversal are congruent, then the transversed lines are parallel.
• Alternate Exterior Angles Converse Theorem: If any pair of alternate exterior angles of a transversal are congruent, then the transversed lines are parallel.
• Alternate Interior Angles Converse Theorem: If any pair of alternate interior angles of a transversal are congruent, then the transversed lines are parallel.
• Consecutive Interior Angles Supplement Converse Theorem: If any pair of consecutive interior angles of a transversal are supplementary, then the transversed lines are parallel.