Identifying Transversals

Illustrated · 1 min

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A transversal is any line that crosses at least two other lines. The following are all transversals:

Three panels, each with a red transversal crossing two blue lines: the lines in the left and right panels are not parallel, while the two horizontal lines in the middle panel are parallel. — The red lines are transversals.

Transversals are usually used in when they cross two parallel lines, as they have some pretty useful properties when this happens. Let's use the following figure for a reference:

Two horizontal parallel lines cut by a slanted transversal, with the eight angles numbered 1 to 8: angles 1 to 4 at the top intersection and 5 to 8 at the bottom.

Vertical angles are equal

Vertical angle are on the opposite sides of an intersection of two lines. Some examples of vertical angle pairs in the above figure are $2, 3$ ; $1, 4$ ; $5, 8$ ; and $6, 7$ . Vertical angles are always equal, and are usually pretty easy to spot, so they're great to keep in mind.

Corresponding angles are equal

Corresponding angles are the angle pairs which are in the same position relative to the transversal. Some examples of corresponding angle pairs in the above figure are $1, 5$ ; $2, 6$ ; $3, 7$ ; and $4, 8$ . Corresponding angle pairs are always equal.

Alternate interior angles are equal

Alternate interior angles are angles that are on different sides of the transversal, and on opposite parallels, but within the middle of the parallel. The pairs of alternate interior angles in the above figure are $3, 6$ and $4, 5$ . They are always equal.

Alternate exterior angles are equal

Alternate exterior angles are angles that are on different sides of the transversal, and on opposite parallels, but on the outsides of the parallels. The pairs of alternate interior angles in the above figure are $1, 8$ and $2, 7$ . They are always equal.

Same-side interior angles are supplementary

Same-side interior angles are the angles which are within the parallels, and on the same side of the transversal. They are supplementary, which mean that add to $180^{\circ}$ or the straight angle.

This is not all of the relationships we can make from a transversal over two parallels. However, these relationships should be enough, when used in conjunction with one another, to derive any other relationship.

Interactive · 1 question

By Elise Molinaro

A transversal is a line that intersects two or more coplanar lines in different points.

Coplanar lines are lines that lie in the same plane.

Two parallel-looking lines, ends labeled A (upper) and B (lower), crossed by a transversal running up to E. Blue point C is on the upper line and purple point D on the lower line.

Three slanted lines: line X crosses lines Y and Z, meeting Y at red point A and Z at green point B, with Y and Z slanting up to the right.

Identify the transversal.