Angle Pairs

A transversal is any line that intersects two or more lines in the same plane but at different points. In Figure 1 , line t is a transversal.

Angle Pairs
A transversal is any line that intersects two or more lines in the same plane but at different points. In Figure 1 , 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 2 , ∠l and ∠5 are corresponding angles. Other pairs of corresponding angles in Figure 2 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.
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