Lesson Video: Congruent Shapes | Nagwa Lesson Video: Congruent Shapes | Nagwa

# Lesson Video: Congruent Shapes Mathematics

In this video, we will learn how to define congruent shapes as shapes that are exactly the same size and shape but may have different colors and orientations.

12:06

### 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.

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