Alternate Exterior Angles

Angles 1 and 8, and 2 and 7 are pairs of alternate exterior angles. They are on opposite sides of the transversal, and on the exterior of the parallel lines.

When AB and CD are Parallel

These eight angles would exist even if lines AB and CD were not parallel. However, when lines AB and CD are parallel, we can draw conclusions about the special angle pairs.

  1. The corresponding angles (1 and 5, 2 and 6, etc.) are congruent.
  2. The alternate interior angles (4 and 5, 3 and 6) are congruent.
  3. The alternate exterior angles (1 and 8, 2 and 7) are congruent.
  4. Interior angles on the same side of the transversal (3 and 5, 4 and 6) are supplementary.
These relationships form the bases of many a geometric proof, so it's important to understand them.