Angle Pairs Created with a Transversal
A transversal is any line that intersects two or more lines in the same plane but at different points. In Figure , line t is a transversal.
Figure 1 A transversal intersecting two lines in the same plane.
A transversal that intersects two lines forms eight angles; certain pairs of these angles are given special names. They are as follows:
- Corresponding angles are the angles that appear to be in the same relative position in each group of four angles. In Figure , ∠l and ∠5 are corresponding angles. Other pairs of corresponding angles in Figure are: ∠4 and ∠8, ∠2 and ∠6, and ∠3 and ∠7.
Figure 2 A transversal intersecting two lines and forming various pairs of corresponding angles
alternate interior angles, alternate exterior angles, consecutive interior angles, and consecutive
exterior angles.
- Alternate interior angles are angles within the lines being intersected, on opposite sides of the transversal, and are not adjacent. In Figure 2, ∠4 and ∠6 are alternate interior angles. Also, ∠3 and ∠5 are alternate interior angles.
- Alternate exterior angles are angles outside the lines being intersected, on opposite sides of the transversal, and are not adjacent. In Figure 2, ∠l and ∠7 are alternate exterior angles. Also, ∠2 and ∠8 are alternate exterior angles.
- Consecutive interior angles (same‐side interior angles) are interior angles on the same side of the transversal. In Figure 2, ∠4 and ∠5 are consecutive interior angles. Also, ∠3 and ∠6 are consecutive interior angles.
- Consecutive exterior angles (same‐side exterior angles) are exterior angles on the same side of the transversal. In Figure 2, ∠l and ∠8 are consecutive exterior angles. Also, ∠2 and ∠7 are consecutive exterior angles.