Video Transcript
Parallel and Perpendicular
Lines
In this video, we’re going to learn
how to describe pairs of lines as parallel or perpendicular. Meet Larry. You know the white lines that are
painted on sports fields. Well, it’s Larry’s job to paint
them there. Today, he’s going to paint the
lines for a running track. One, two. Oh, dear, that’s no good,
Larry. You’ve made a mistake here. The lines of a running track always
need to be the same distance apart. But the way Larry’s painted these
lines, they’re not always the same distance apart at all. Try again, Larry. Those lines are much better.
Can you see that this pair of lines
are always the same distance apart? No matter how long Larry keeps
painting for, these two lines are never going to cross. We call lines like this parallel
lines. And inside the word “parallel,”
there’s a little clue to help us remember what it means. Can you see the two letter l’s next
to each other? These two letters are straight
lines that are always the same distance apart, aren’t they? Even the letter l’s in the word
parallel are parallel. Now there’s a way that we can show
that our lines are parallel, and that’s to draw two little arrow heads, one on each
line. Whenever we see lines labeled like
this, we know that they’re parallel.
Now, Larry is going to paint the
lines on a football field. One, two. Now, does that corner look right to
you? It doesn’t, does it? These two lines need to make a
square corner. That’s much better. The two lines that join at the
corner of a football field make a right angle. In maths, we describe two lines
that join at a right angle using the word perpendicular. This is a fun word to say. Let’s try splitting it up into each
different syllable, PER-PEND-IC-U-LAR, perpendicular. We can say that these two lines are
perpendicular because they meet at a right angle. And we can show that two lines are
perpendicular by drawing a little right-angle sign, which is a square, where they
meet.
So wherever we see this symbol, we
know that the two lines are at right angles to each other. They’re perpendicular. A really good, real-life example of
the sorts of lines we’ve been talking about is a railway line. And we’re looking down on this
railway line from above. But can you see that two tracks
that make up our railway line are always the same distance apart? And you know, railway tracks always
have to be the same distance apart. Otherwise, the train would come off
the tracks, wouldn’t it? Because our tracks are always the
same distance apart and will never ever cross, we can describe them as being
parallel. But don’t forget. We don’t need to label them using
words. Instead, we can show that these two
lines are parallel by drawing two little arrow heads.
Now, by looking at the picture, we
can see straightaway that the pink lines or the railway tracks are parallel. Now, can you see any perpendicular
lines on this picture? There are actually lots of
them. Each of the railway sleepers is a
rectangle. And we know that a rectangle has
square corners. So we can see that these two sides
of this sleeper meet at a right angle. They’re perpendicular. But rather than writing out that
long word all the time, we can simply show that these lines meet at a right angle by
drawing a little right-angle symbol or a square where they meet.
And can you see that the line where
the sleeper meets the track is also a right angle. There are lots of parallel and
perpendicular lines in this picture, aren’t there? Have a look around you. They’re all over the place, books
on a shelf, the fence in your garden, even the screen that you’re watching this
video on. These two sides of the video screen
meet at a right angle. And there are lots more to find if
we carry on looking around the screen. These are all examples of pairs of
perpendicular lines. And if we’re looking for parallel
lines on our video screen, we can see that the two sides of the screen are parallel
and also the two sides at the top and bottom of the screen are parallel too.
Do you think you’ve learned now how
to spot parallel and perpendicular lines? Let’s have a go at answering some
questions now where we have to put into practice what we know of pairs of parallel
and perpendicular lines. Try saying that fast.
These lines are perpendicular. What type of angle is highlighted
in red?
The first sentence in this question
contains a really interesting word “perpendicular.” Now, we’re told that these lines
are perpendicular, but which lines is it describing? Well, if we look in the picture, we
can see two lines. We’ve got one that’s vertical that
goes up and down. And we’ve also got a horizontal
line that has been drawn from left to right. Now, what can we say about these
lines? Well, firstly, we can see that
they’re straight lines. They’re not curved at all, are
they? We can also see that these two
lines meet together. In fact, they cross over each
other, don’t they?
Now, there are lots of ways we
could draw two lines that cross over each other, like this or this. But the two lines in our picture
are interesting because they meet in a special way. When two lines are perpendicular,
we know that they meet at right angles. But imagine that we read this first
sentence and we didn’t know what the word “perpendicular” means. Can you see another clue that helps
us? This little symbol here is the
symbol for right angles. So even if we’re not quite sure
what the word “perpendicular” means, we could look at the diagram, see this little
symbol, and think to ourselves, “I know that these two lines meet at right
angles.”
Now, our question asks us, what
type of angle is highlighted in red? Can you see what this is talking
about? It’s this angle here. How could we describe this
angle? Well, because we know that these
two lines are perpendicular, we can draw little right-angle symbols at all the
places where they meet. The angle that’s shown in red is a
right angle. When two lines are perpendicular,
they meet at right angles. And that’s how we know the type of
angle that’s highlighted in red is a right angle.
Complete using “parallel” or
“perpendicular”: The two red-colored lines are what.
This is an interesting four-sided
shape, isn’t it? You might not know the name of it,
but it doesn’t matter, because in this question, all we need to think about are the
two red-colored lines that we can see that make up the sides of the shape, here and
here. Now, we need to describe these two
lines. And we’re told that we have to
complete the sentence using either the word “parallel” or “perpendicular.” Do you remember what these two
words mean?
Parallel lines are always the same
distance apart. They can never ever cross. But perpendicular lines do
touch. In fact, they meet at right
angles. And if we look at our two
red-colored lines, we can see straightaway that they don’t meet at right angles. In fact, they’re not touching at
all, are they? They must be the same distance
apart. Now, if we look at the top and the
bottom of the two red lines, it does look like they’re the same distance apart. But without a ruler, how can we
tell?
Well, there’s a clue in the
picture. We know that whenever we see a pair
of lines labeled using arrow heads like this, they are parallel. So we can see that they’re the same
distance apart. But we can also see that they’ve
been labeled to show this. The two red-colored lines are
parallel.
Complete using “parallel” or
“perpendicular”: The two red-colored lines are what.
In this question, we’re given a
picture of a shape, and two of its sides are colored red. Now, how can we describe these two
red-colored lines? Are they parallel? Or are they perpendicular? We know that when two lines are
parallel, they’re always the same distance apart. So if we think about this red line
here to begin with, a line that’s parallel to this line might look like this, or
even this. Or if we look at the red line at
the bottom of our shape, a line that’s parallel to this might look like this or even
this.
But when we look at the two lines
together and compare them, we can see that they’re not parallel with each other at
all, are they? Just like two railway tracks,
parallel lines never touch. But we can see that these two lines
do touch. In fact, where they meet, a little
symbol’s been drawn. Do you remember what this symbol
means? It’s the symbol we use to show a
square corner or a right angle. And we know that the word we use to
describe a pair of lines that meet at a right angle is “perpendicular.” These two sides of the shape meet
at a right angle. And so we can say the two
red-colored lines are perpendicular.
Which of the following letters has
parallel lines: Y, F, A, or L?
Now, we know when two lines are
parallel, they’re always the same distance apart. So when we look at them, they look
like they’re going in exactly the same direction. These two lines are parallel, so
are these. But we couldn’t say that these two
lines are parallel because these aren’t always the same distance apart. Now, in our question, we’re given
some capital letters to look at. And we’re asked which one of them
has parallel lines. Now, to help us answer the
question, let’s write these capital letters really big. And we’re going to use a different
color for each line that makes up the letter.
To begin with, we’ve got the letter
Y. Now, we can write the letter Y by drawing a straight line up like this and two
lines at the top that make a sort of V shape. Now can you see any pairs of lines
in this letter that are always the same distance apart, they never touch, and
they’re going in the same direction? We can’t, can we? If we look at the pink line and the
orange line, well, they’re touching, and they’re not the same distance apart. And the same is true of the green
line and the orange line. And even if we look at the pair of
lines that make the V shape, that’s the pink line and the green line, we can see
that the distance between them isn’t always the same at all. The letter Y doesn’t have any
parallel lines.
What about the letter F? We can write a capital F by drawing
a straight line upwards and then two shorter horizontal lines. Can you see any parallel lines in
this letter? If we look at the orange line and
the pink line to begin with, we can see that they meet at a right angle. They’re not parallel, but we could
describe them as being perpendicular. Unfortunately, though, we’re not
looking for perpendicular lines, which is a shame because the orange line and the
green line are perpendicular too.
Now, what if we compare the green
line and the pink line? We can see that they are always the
same distance apart, and they do go in the same direction. These two lines are parallel. And we can show that they’re
parallel by drawing little arrow heads, one on each line. Wherever we see lines labeled like
this, we know they’re parallel. Looks like we found our answer,
doesn’t it? Let’s just check the other
letters.
We can see that in the letter A,
none of the lines are parallel. And the two lines that make up the
letter L aren’t parallel either. We could say they’re perpendicular,
though. They meet at a right angle, don’t
they? Out of the four letters that we’re
given, the one that has parallel lines is the letter F. And if you get a spare
moment, why not see if there are any other letters of the alphabet that have
parallel lines, too?
Determine the colors of the lines
that are perpendicular to each other.
In the picture, we can see three
different colored lines: blue, black, and yellow. The question asks us to find the
colors of the lines that are perpendicular to each other. We know that when two lines are
perpendicular to each other, they’re at right angles with each other. Now, there’s something interesting
about these three lines. None of them are touching, are
they? This makes it a little more
difficult to spot whether they’re at right angles to each other. How can we spot a right angle?
You know, if we’re ever not sure
whether an angle is a right angle or not, we can always just take the corner of a
piece of paper, just like the one we’ve ripped off here. And we can see whether it fits
between two lines because we know the corner of a piece of paper is a square corner
or a right angle. Let’s think of this corner of a
piece of paper as a special right-angle tester.
Can you see where we could place it
on our picture? Here’s a clue. You’re going to have to turn it
slightly. It fits here, doesn’t it? Although the lines aren’t touching,
we can see that the blue and the black lines are perpendicular to each other. And we can see that if we continued
the black line so that the lines did cross, they’d meet at a right angle. The colors of the lines that are
perpendicular to each other are blue and black.
So what have we learned in this
video? We’ve learned how to describe pairs
of lines as parallel or perpendicular.
