How do you prove lines parallel?

Question

When 2 lines are cut by a transversal, how do you prove them parallel? like what theorems, about how many steps, maybe an example?, etc.

Answer 1

if 2 lines are cut by a transversal then all you have to do is prove that the alternate interior angles are the same.



Alternate interior angles are 2 angle on opposite sides of the transversal that are inbetween the 2 lines.

Answer 2

Okay.. well first of all, if there is a transversal cut through 2 lines, it cuts each line in 2 pieces.

_________ /______

-----------a-- / b

--------------/

____ c _/_d________



/ = transversal

a, b, c, d = angles

___ = lines awaiting to be proven parallel



*Please ignore the -----

*If you do not undrstand the picture, refer to this website,http://i.ehow.com/images/GlobalPhoto/Articles/4851277/paratransversal_Full.jpg

and look at the angles correspoding the the picture i made.



As you can see, one line cuts 2 lines. The 4 letters represent the angles.

You can show that a + b = 180 degrees because a line is 180 degrees, as you know.



Then, c + d = 180 as well because of what we just said. So then, we look at if a = d.

If angle a is the same as d, then you can prove that the lines are parallel because of the rule of Oposite Interior angles. That is if opposite interior angles are congruent, then the lins are parallel.



You can do the same thing with b and c, as well. Also, later you will learn that exterior angles do the same thing, but a little opposite. If same side exorior = 180 degrees, then the lines are parallel and if opposite exterior angles are congrent, then the lines are parallel aswell.

Lol, i know its a lot but it comes pretty easily if you have a diagram in front of you.

Answer 3

parallel lines have the same slope. you need two points on those two lines for them to be parallel. you get the two points, subtract the x's, then subtract the y's and put it in a fraction with the y change on top. then you have your slope. do the same for the other line and if you end up with the same fraction then theyre parallel.

Answer 4

http://www.youtube.com/results?search_query=How+do+you+prove+lines+parallel&search_type=&aq=f





http://en.wikipedia.org/wiki/Parallel_postulate



http://jwilson.coe.uga.edu/emt668/EMAT6680.2001/Meyers/EMAT%206700/EMAT6700f.html