Parallel LinesDate: 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/ |
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