Two lines are perpendicular when they cross at a right angle (checked with the set square, marked with a little square). Two lines are parallel when they run in the same direction and never cross — like the two rails of a track, always at the same distance from each other.
Examples
Example 26.3 (Spotting them in figures)
In a rectangle, each side is perpendicular to its two neighbors and parallel to the opposite side. Grid paper is a ready-made network of parallels and perpendiculars — that is what makes it so comfortable to draw on.