What is the difference between alternate and corresponding angles?

Jan 7, 2016

See the picture and explanation below.

Explanation:

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.