Parallel and perpendicular lines are special pair of lines. Do you know about their special properties?
Parallel Lines
Parallel lines are lines that are on the same plane and never intersect. Parallel lines have an equal distance separating them e.g. in the following figure, lines 
and 
are parallel to each other and there is a unique distance " 
" between the two lines.
and are parallel to each other and there is a unique distance " " between the two lines.
Perpendicular Lines
Two lines are perpendicular if they intersect and form a right angle at the point of intersection. In the following figure, lines and are perpendicular to each other and measure of angle 
and are perpendicular to each other and measure of angle 
Parallel and perpendicular lines are the basis for advanced concepts such as pair of angles and slope of parallel and perpendicular lines in coordinate geometry. We will come to these lessons later. However for now you should remember the following points about parallel and perpendicular lines:
- Parallel lines never intersect each other and there is a uniform distance between these two lines.
- When two lines that are perpendicular intersect, the angle of intersection is always a right angle.
Let us consider a very easy example to test this concept:
Example:
There are 3 parallel lines drawn on a plane. If another set of 4 parallel lines are drawn such that the new set of lines are perpendicular to the original set of lines, how many points of intersections exist on the plane?
A) 0
B) 1
C) 7
D) 12
E) 24
Solution:
This problem expects you to apply your knowledge of parallel and perpendicular lines. You should know that every line that is drawn perpendicular to the original set of 3 parallel lines will create 3 points of intersection. Therefore the new set of lines will create a total of 4 × 3=12 points of intersection. You can visualize the points of intersection in the following figure:
D is the correct answer.
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