Video Transcript
Congruent Shapes
In this video, we’re going to learn
how to define congruent shapes as those that have exactly the same size and
shape. And we’re also going to learn that
congruent shapes may have different colors and also be shown in a different
position.
Let’s start by thinking a little
more about the cartoon that we’ve just seen on our title page. I don’t know whether you had one of
those toys when you were little that featured lots of holes in different shapes and
you had some colored 3D shapes to put in those holes. It’s a sort of toy little children
use to learn about sorting and matching. Well, in our cartoon, we’ve got a
similar sort of thing going on. We’ve got a character holding a
shape. This isn’t a 3D shape, though, is
it? It’s a flat 2D shape. And then we’ve got several shapes
on the wall. It looks like this is some sort of
TV game show, and the contestant doesn’t have very long left to make a decision.
This video is all about shapes that
are what we call congruent. And you know if we can understand
where this contestant needs to place the shape in their hand and why, we’re one step
along the way to understanding what the word congruent means. Let’s take a closer look at this
shape. This is a six-sided shape, which
means it’s a hexagon. And although hexagons come in all
sorts of different shapes, the lengths of the sides of this are all the same; it’s
what we call a regular hexagon.
Now, if we look at the shapes on
the wall, perhaps you can see that there are two possibilities. We can see straightaway that three
of the shapes don’t actually have six sides, so we can forget them. But two of our shapes do have six
sides, and they’re all the same length too. These are both examples of regular
hexagons, but there are some differences. Can you spot them? Our first hexagon is exactly the
same size as the one that the monster’s holding. And it’s exactly the same shape
too. The only difference is it’s being
turned slightly, is in a slightly different position. So, for our contestant to match the
shape, they just have to turn it slightly.
Our second possible answer again is
the same shape. It’s a regular hexagon, and it also
looks like it’s in the same position. But there is a difference here. This regular hexagon is a different
size to the one we’re looking to match. For us to match the shapes exactly,
we need to make our shape a lot bigger. So, which out of the two would you
choose? Our pink regular hexagon is the
same as shape one. They fit perfectly together. They’re the same size and exactly
the same shape. Yes, they’re in a slightly
different position, but we can turn the shape, can’t we? And when we do, we can see that
they match.
So, what’s a pretend TV game show
got to do with this idea of congruent shapes? Well, just like our hexagons,
shapes that are congruent are exactly the same size and exactly the same shape. It doesn’t matter if they’re
different colors, and it doesn’t matter if they’re shown in different positions. If two shapes are exactly the same
size and also exactly the same shape, we call them congruent.
Here’s another way to help us
understand what the word congruent means, and it’s all to do with making congruent
shapes of our own. Let’s imagine that we take a piece
of paper, we draw a line down the center, and we fold it in half. And then, on top of our folded
piece of paper, we draw a shape, perhaps a kite shaped like this. Next, we take a pair of scissors
and we cut out our kite shape. Or should we say, kite shapes? Because we folded our piece of
paper in half, we’ve got two of them. The way that we’ve cut out the
shapes means that we know they’re exactly the same size and exactly the same
shape. They are what we call
congruent.
It doesn’t matter if someone comes
along and turns one of the shapes slightly or even flips it upside down. We could even take a pen and shade
it in a completely different color. Our shapes are in different
positions and they’re different colors. But if we flip one of our shapes
and rotate it, we can show that both shapes will fit perfectly on top of each
other. They’re exactly the same size and
exactly the same shape; they’re congruent. But what if we can’t cut out the
shapes that we’re given? Maybe they’re in the maths
book. What else could we do to see if
they match?
Here is an image of two shapes. But are they congruent or not? And how can we tell? Well, one way that we could test to
see is to take a piece of tracing paper or some sort of other paper that we can see
through and to trace the outline of one of the shapes, making sure that we do so
really accurately. So, we’re going to use a ruler. Here we are. We can then move our tracing
towards the other shape. We want to see if it fits. We may need to rotate it. We may even need to turn our
tracing paper upside down and then move it some more.
Our tracing of one of the shapes
fits perfectly on top of the other shape. We may have had to turn it a
little; we may have had to flip it over. But both our shapes are exactly the
same size and exactly the same shape; they are congruent. Now, do you think you’ve got the
hang of spotting congruent shapes? Let’s have a go at answering some
questions that are all about trying to identify them.
Are the two shapes congruent?
In the picture, we can see two 2D
shapes and we’re asked a simple yes-no question, “are they congruent?” To answer the question correctly,
we’re going to need to remind ourselves what the word congruent means. Congruent shapes are exactly the
same shape and exactly the same size. Now, we don’t need a ruler to
compare the size of these shapes. Would you say they’re the same
size? They’re not, are they?
Just by looking at the shape on the
right, we can see that it’s smaller. If our two shapes with the same
shape, then they’d match exactly if one was put on top of the other. But take a moment and look at our
shapes. Does it look like one would fit on
top of the other? This is where the skill of being
able to visualize shapes comes in useful. Imagine that we could take the
shape on the right and move it across until it was on top of the shape on the
left. Would it fit? No, it wouldn’t. We can see that the sides have
matched up, but the base and the top part of our shape isn’t.
What if we turned our shapes
slightly? Would the two shapes match
then? Not at all. We can tell just by looking at
these two shapes, they’re not exactly the same shape and they’re not exactly the
same size. The answer to this question is “no,
these two shapes are not congruent.”
Which two figures are
congruent?
In the picture, we can see three
shapes or figures, and they’re labeled (a), (b), and (c). And we’re asked, which two of these
are congruent? We know that for two shapes to be
congruent, they need to be exactly the same size and exactly the same shape. Now, if we want to compare the
three shapes that we’ve been given, there’s something in the picture that’s there to
help us. Can you see what it is? All three shapes have been drawn on
some squared paper, and this is really going to help us when it comes to the same
size part of the definition.
Now, how would you describe these
shapes? Well, all three look like they
belong to the same sort of family, don’t they? They’re all this sort of U
shape. It’s a little bit like a rectangle
or square, with a part missing at the top. Each one has got eight sides. They’re not all the same length, so
we know that they’re irregular octagons. But which two are exactly the same
size and shape? Perhaps you can see the answer just
by looking, but let’s use our squares to help us and prove which two are the
same.
If we look at the base of our first
shape, we can see that it’s three squares long. The base of the second shape is
four squares long, and the base of shape (c) is three squares long. It looks like shapes (a) and (c)
might be congruent, isn’t it? We better check, though, by looking
at all of the sides. The straight side on the left is
four squares long in shape (a). We can see this is the same with
shape (c). And if we carry on comparing each
of the sides, we can see that they match every time. Not only are shapes (a) and (c) the
same shape, they’re also exactly the same size. We can describe them as
congruent. The two figures that are congruent
are (a) and (c).
Which shape is not congruent to the
others?
This problem is a sort of
odd-one-out question. We’re given some shapes and we need
to find the one that’s different. This is because when shapes are
congruent, we know they’re exactly the same size; they’re exactly the same
shape. So, four out of our five shapes are
exactly the same size and shape. But one of them is not
congruent. We’re looking then for the shape
that’s different.
Now, as we’ve just said, there are
two parts, two shapes, being congruent. They must be the same size, and
they must be exactly the same shape. It doesn’t matter what color they
are; it doesn’t matter what position we put them in. But those two factors must be
true. Now, if we look at our five shapes,
we can see that they’re all in different positions. As we’ve just said, this doesn’t
mean they can’t be congruent. We know that two shapes can be
exactly the same, but just in a different position. But it does make them harder to
spot.
One way that we could check which
of these shapes are the same even though they’re in different positions would be to
put a little piece of tracing paper or some sort of paper we can see through over
one of the shapes then trace it and then move it to see if it fits exactly on top of
any of the other shapes. For example, we’ve just proved that
shapes (a) and (d) are congruent.
But you know, perhaps there’s a
quicker way to find the answer here, because not only the shapes need to be exactly
the same shape to be congruent, they need to be exactly the same size. And one of these shapes is not the
same size as any of the others. We don’t need to get a ruler or
anything like that. We can see just by looking with our
eyes that shape (b) is larger than any of the other shapes. So, although we could go from (a)
to (e) and check whether they’re exactly the same shape, perhaps using tracing
paper, we’ve identified what we could call the odd one out because it’s not the same
size as any of the others. The shape that is not congruent is
shape (b).
What have we learned in this
video? We’ve learned how to define
congruent shapes as shapes that are exactly the same size and exactly the same
shape, regardless of their color or their position.
