When a transversal (any line that passes through two parallel lines) cuts two parallel lines then the angles that correspond to the similar positions (angles in the matching corners) with respect to either of the parallel lines and lie on the same side of the transversal are called the Corresponding angles. The angles lie on the same side of the parallel lines.
Corresponding Angles
In this figure, Line m and line n are parallel. The transversal cuts both the lines. $\angle$b and $\angle$f are angles formed when the transversal cuts m and n and these are one pair of angles that correspond to the similar position (above m and above n) and lie on the same side of the transversal. Thus $\angle$b and $\angle$f are corresponding angles. There are many other pairs of corresponding angles in this figure. $\angle$a and $\angle$e; $\angle$c and $\angle$g; $\angle$d and $\angle$h are the other pairs of corresponding angles in this figure.

To identify the corresponding angles it is easy by writing the letter F along the two parallel lines and to identify the angles around the corners of the two horizontal lines of F and the transversal. The letter F can be written on either ways on the parallel lines.
Corresponding Angle

If two parallel lines are cut by a transversal, then the pairs of corresponding angles are always congruent.Postulates are not proved, but are assumed to be self-evident and true. So pairs of angles which lie on the same side of transversal and the same side of both parallel lines are congruent.

Corresponding Angles Postulates

In this figure, two lines m and n are cut by the transversal l,
if m || n, then $\angle$1 $\cong$ $\angle$2