To intercept something is to take it while it is in the process of going somewhere; typically, you can intercept a message. If you steal a letter out of someone's mailbox, you have intercepted their mail (don't do this). Intersecting is a term from geometry. It means to go through something, particularly, a line that goes through another line.
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The intersecting lines of a rectangle are at ninety degrees while the intersecting lines that form a parallelogram may be greater than or less than ninety degrees.
perpendicular crosses at a right angle, while intersecting lines don't
Perpendicular lines are a subset of intersecting lines. The only difference is that perpendicular lines intersect at an angle of 90o, whereas intersecting lines can converge at any angle.
Vertex
parallel