Parallel Lines

Date: 12/31/98 at 11:44:11
From: Corey McHatton
Subject: (Geometry) - Parallel lines

What are some ways of proving lines parallel?

Date: 01/22/99 at 11:18:01
From: Doctor Maryanthe
Subject: Re: (Geometry) - Parallel lines

Hi Corey,

Thanks for writing Dr. Math!

There are lots of ways to prove lines parallel. It depends on what you 
are given to work with. Are you using coordinates and equations in 
algebra, or drawing lines and looking for similar angles in geometry? 

I'll get you started by listing a couple of different ways to prove 
lines parallel, using several different methods. If you have any 
questions, please write back.

1. SLOPE 

If both lines have the same slope, they are parallel. So, if you know 
the equations for both lines, and you can see that both equations have 
the same slope, you know the lines are parallel.

2. USING OTHER LINES - Similar angles  

Suppose we have three lines again all in the same plane, A, B and C. 
If line B makes a 30-degree angle on the left with line A, and also a 
30-degree angle on the left with line C, then A and C are parallel. 
This method can also be applied for lines that are perpendicular (form 
90-degree angles).

Here is something else to keep in mind. Remember that parallel in 3 
dimensions is more complicated than parallel in 2 dimensions. In 2 
dimensions, if two lines never intersect, you know they are parallel. 
In 3 dimensions, it is possible to have two lines that never intersect 
but are not parallel. This is called skew. Can you visualize it?

How many other ways can you think of to prove lines parallel?

Good luck!

- Doctor Maryanthe, The Math Forum
  http://mathforum.org/dr.math/