Trains and Railroads

# Beth thinks that a train tracks run parallel to each other kim thinks that they run perpendicular to each other who is correct?

###### Wiki User

###### December 15, 2008 9:25PM

Neither. They run paralevel with one another.

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### Are railway lines parallel or perpendicular?

Railway lines are parallel. 2 lines are said to be parallel when they are
contained in the same plane and do not intersect. This is the
definition. That parallel lines exist is an assumption (postulate)
of Euclidean geometry:
Parallel lines are like the rails of a train track, and you
might think of defining them this way, as lines that are the same
distance apart everywhere. The problem with this kind of definition
is it assumes both tracks are straight. Though this seems an
obvious possibility, when you go into the vast universe it is not
that obvious. Parallel lines puzzled the best mathematicians for
centuries until it was realized that we must assume they
exist (you can't prove they exist from simpler postulates). The
problem with parallel lines lies in the notion that the lines have
infinite extent.
Euclid used a somewhat different parallel postulate in trying to
avoid the notion of the infinite. He observed that when two
parallel lines are intersected by a third line, called a
transversal, then if you measure two angles formed by these
three lines, on the same side of the transversal and between the
parallels, they will add to (that is, they will be supplementary).
Such angles are called same-side interior angles.Another
important concept is perpendicular. By definition, two lines
are perpendicular if they intersect at right angles. That
is, two perpendicular lines form 4 right angles. Segments and rays
can also be perpendicular. This means they intersect in at least
one point, and the two lines containing them are perpendicular.
We use perpendicular segments to measure the distance from a
point to a line, a point to a plane, or the distance between two
parallel lines or planes. The ties of a railroad track are
perpendicular to the rails and of the same length. This common
length is the distance between the rails. (If parallel lines exist,
then railroad tracks in space can go on forever.)
There are three theorems about perpendicular lines that you
should know. We will not attempt to prove them here, but if you
think about them they should be rather obvious.We can use this fact
to define the distance from a point to a
line: That distance is the length of a segment perpendicular to
the line with the given point as one of its endpoints and the other
endpoint on the line. In fact, a similar notion holds in 3
dimensions. If we have a plane and a point not on that plane, then
there is only one line through the point perpendicular to the
plane, and the length of the segment determined by that point and
the intersection of the perpendicular line with the plane is
defined as the distance from the point
to.