# What lines, segments, or rays are parallel in figure #13 in the following link? What postulate or theorem proves them parallel?     ...

What lines, segments, or rays are parallel in figure #13 in the following link?

What postulate or theorem proves them parallel?

http://media.cheggcdn.com/media/194/1941e517-b09f-4759-9cb1-6a033756def8/phpFZgyq2.png

I just need an explanation as to why they are parallel.

I believe segment LO is parallel to segment JN and ray LM is parallel to ray JK by the corresponding angles converse postulate.  Am I right?

I would really appreciate help on this!

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You should notice that if the lines LO and JN would be parallel, then the angle made by LO with transversal line needs to be equal to the angle made by JN with the same transversal line, as corresponding angles.

Notice that the angle made by LO with the transversal line is of `42^o`  while the angle made by JN with the transversal line is of `38^o` , hence, they are not equal, then the lines JN is not parallel to LO.

Notice that the angle made by ML with the transversal line is of `28^o+42^o = 70^o`  and the angle made by KJ with the transversal line is of `32^o + 38^o = 70^o` , hence, the angle are corresponding and the lines are parallel, `ML || KJ` .

Hence, evaluating the pairs of parallel lines based on the pairs of angles formed when a transversal crosses the given lines, yields that `ML || KJ` .