What is the difference between alternate and corresponding angles?

When two parallel lines are intersected by the third (transversal), they form eight angles: one of the parallel lines forms four angles #a#, #b#, #c# and #d#, another forms angles #a'#, #b'#, #c'# and #d'#.

Two acute angles #a# and #a'#, formed by different parallel lines when intersected by a transversal, lying on the same side from a transversal, are called corresponding.
So are other pairs (acute and obtuse) similarly positioned: #b# and #b'#, #c# and #c'#, #d# and #d'#.
One of corresponding angles is always interior (in between parallel lines) and another - exterior (outside of the area in between parallel lines).

Two acute angles #a# and #c'#, formed by different parallel lines when intersected by a transversal, lying on the opposite sides from a transversal, are called alternate.
So are other pairs (acute and obtuse) similarly positioned: #b# and #d'#, #c# and #a'#, #d# and #b'#.
The alternate angles are either both interior or both exterior.

The classical theorem of geometry states that corresponding angles are congruent. The same for alternate interior and alternate exterior angles.