Parallel lines are lines that stay the same distance apart, no matter how long you draw them in either direction, i.e.:
Parallel lines are marked with arrow heads.
If there are 2 sets of parallel lines in a diagram, on the 2nd set of parallel lines, use double arrows instead of single arrows, i.e.:
A line which cuts a pair of parallel lines is called a transversal. For example, the green line below is the transversal line:
Corresponding angles are those which correspond to the same location, with respect to the transversal line, and the parallel lines, e.g.:
The corresponding angles are equal to each other. Note that apart from the 2 corresponding angles listed, there are 4 others, representing the 4 different points of the X (where the green and red lines meet).