What is the difference between alternate and corresponding angles?

See the picture and explanation below.

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.