Knowing How Angles, Lines, and Transversals Relate

By Carla Kirkland, Chan Cleveland

A transversal is a line that intersects at least two other lines at a different point for each. That situation involves multiple angles and angle relationships.

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The transversal in the diagram is the line that goes down and to the right. The lines intersected by the transversal are the horizontal lines. Several types of angle pairs exist in the scenario:

  • Alternate interior angles, such as Angle 4 and Angle 5, are on alternate sides of the transversal and are interior to the lines that are intersected.

  • Alternate exterior angles are on alternate sides of the transversal and are exterior to the lines that are intersected. Angle 2 and Angle 7 make up an alternate exterior angle pair.

  • Corresponding angles, such as Angle 3 and Angle 7, are on the same side of the transversal and formed by it but are formed by different lines that the transversal intersects. In other words, they are formed exactly the same way except by different intersected (by the transversal) lines.

  • Consecutive interior angles are pairs that are on the same side of the transversal and interior to the lines intersected by the transversal. Angle 4 and Angle 6 make up a pair of consecutive interior angles.

Okay, here are the rules. All pairs of alternate interior angles, alternate exterior angles, and corresponding angles are congruent pairs if the lines the transversal intersects are parallel, in which case each pair of consecutive interior angles are supplementary. That’s four rules right there.

Here are four more. If any of those pairs is congruent or supplementary, the lines the transversal intersects are parallel. For example, if the alternate interior angles 3 and 6 are congruent, the lines the transversal intersects are parallel.

Vertical angles are always congruent, and any two angles that form a linear pair are supplementary. When you know all these rules, you can take the measure of any angle in the diagram and determine the measures of all the other angles as long as the lines intersected by the transversal are parallel.