Definitions and Angle Relationships Formed by a Transversal

Transversals and Line Intersections

A transversal is defined as a line that intersects two or more lines at different points. When a transversal crosses a set of coplanar lines, it creates distinct intersection points and angle configurations that form the foundation of planar line geometry.

Table of definitions and diagrams for transversal angle relationships

Corresponding Angles

Corresponding angles are defined as two angles that lie on the same side of the transversal in corresponding positions. In an intersection of two lines by a transversal, angles residing in matching relative quadrants at each intersection—such as both in the upper-right or both in the lower-left—are corresponding angle pairs.

Alternate Interior Angles

Alternate interior angles are defined as interior angles that lie on opposite sides of the transversal. These angles sit inside the region bounded between the two main lines and lie on opposite (alternate) sides of the intersecting transversal line.

Alternate Exterior Angles

Alternate exterior angles are defined as exterior angles that lie on opposite sides of the transversal. These angles are positioned outside the space between the two intersected lines and lie on opposite sides of the transversal line.

Supplementary Angles

Supplementary angles are defined as two (or more) angles whose sum is $180^\circ$ . When two angles are supplementary, their degree measures combine to equal a straight angle, satisfying the relationship $\theta_1 + \theta_2 = 180^\circ$ .

Vertical Angles

Vertical angles are defined as two angles whose sides form opposite rays. Vertical angles are created opposite each other whenever two straight lines intersect, sharing a vertex without sharing any common sides.

Consecutive Interior Angles

Consecutive interior angles are defined as angles that lie on the same side of the transversal between two lines. Also referred to as same-side interior angles, these reside entirely within the interior region bounded by the two intersected lines and stay on the identical side of the transversal.