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CCSS.Math:

Identify all sets of
parallel and perpendicular lines in the image below. So let's start with
the parallel lines. And just as a
reminder, two lines are parallel if they're
in the same plane, and all of these lines are
clearly in the same plane. They're in the
plane of the screen you're viewing right now. But they are two lines that
are in the same plane that never intersect. And one way to verify,
because you can sometimes-- it looks like two
lines won't intersect, but you can't just always
assume based on how it looks. You really have to
have some information given in the diagram or
the problem that tells you that they are
definitely parallel, that they're definitely
never going to intersect. And one of those
pieces of information which they give
right over here is that they show that
line ST and line UV, they both intersect line
CD at the exact same angle, at this angle right here. And in particular,
it's at a right angle. And if you have two lines
that intersect a third line at the same angle--
so these are actually called corresponding angles
and they're the same-- if you have two of these
corresponding angles the same, then these two
lines are parallel. So line ST is
parallel to line UV. And we can write it like this. Line ST, we put the arrows
on each end of that top bar to say that this is a line,
not just a line segment. Line ST is parallel to line UV. And I think that's the
only set of parallel lines in this diagram. Yep. Now let's think about
perpendicular lines. Perpendicular lines
are lines that intersect at a 90-degree angle. So, for example, line ST is
perpendicular to line CD. So line ST is
perpendicular to line CD. And we know that they
intersect at a right angle or at a 90-degree angle
because they gave us this little box here
which literally means that the measure of this
angle is 90 degrees. By the exact same argument, line
the UV is perpendicular to CD. Let me make sure I
specified these as lines. Line UV is perpendicular to CD. So I did UV, ST, they're
perpendicular to CD. And then after that, the
only other information where they definitely tell us
that two lines are intersecting at right angles
are line AB and WX. So AB is definitely
perpendicular to WX, line WX. And I think we are done. And one thing to think
about, AB and CD, well, they don't even
intersect in this diagram. So you can't make any
comment about perpendicular, but they're definitely
not parallel. You could even
imagine that it looks like they're about to intersect. And they give us no
information that they intersect the same lines at
the same angle. So if somehow they told us that
this is a right angle, even though it doesn't look
anything like a right angle, then we would have to
suspend our judgment based on how it actually
looks and say, oh, I guess maybe those
things are perpendicular, or maybe these two
things are parallel. But they didn't tell us that. And that would
actually be bizarre because it looks
so not parallel. And actually then
this would end up being parallel to other things
as well if that was done. It's a good thing
that wasn't because it would look very strange. But based on the
information they gave us, these are the parallel and
the perpendicular lines.