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Perpendicular and Parallel

Perpendicular

It just means at right angles (90°) to.

The red line is perpendicular to the blue line in both these cases:

Perpendicular Example 1 Perpendicular Example 2

(The little box drawn in the corner, means "at right angles", so we didn't really need to also show that it was 90°, but we just wanted to!)

Parallel

Lines are parallel if they are always the same distance apart (called "equidistant"), and will never meet. (They also point in the same direction). Just remember:

Always the same distance apart and never touching.

The red line is parallel to the blue line in both these cases:

Parallel Example 1 Parallel Example 2
Example 1
Example 2

Perpendicular to Parallel

Question: What is the difference between perpendicular and parallel?
Answer: 90 degrees (a right angle)

That's right, if you rotate a perpendicular line by 90° it will become parallel (but not if it touches!), and the other way around.

Perpendicular Rotate 90 Degrees

Parallel
Perpendicular ...
Rotate One Line 90°
... Parallel !

 

Parallel Curves

Curves can also be parallel when they are always the same distance apart (called "equidistant"), and never meet. Just like railroad tracks.

The red curve is parallel to the blue curve in both these cases:

Parallel Curves Example 1 Parallel Curves Example 1

 

Parallel Surfaces

Surfaces can also be parallel, so long as the rule still holds: always the same distance apart and never touching.

Parallel Surfaces

Mind Bender

Something that makes my mind bend: we know that if we have two parallel lines, and we rotate one by 90°, they will be perpendicular to each other, right? Well, does the same apply to curves? Can you have "perpendicular curves", by rotating one of them by 90°? I simply don't know, but it is fun to think about.