Video: Properties of 2D Shapes

In this video, we will learn how to analyze 2D shapes to see what features a shape always has and what features it sometimes, or never, has.

15:38

Video Transcript

Properties of 2D Shapes

In this video, we’re going to look carefully at 2D or flat shapes to see what features a shape always has and what features it sometimes or never has.

Oh dear! This is not good. 30 seconds into the video and we’ve already got a mistake. This isn’t a triangle, is it? It’s a square. But how do we know it’s a square? What makes a square square? And what makes a triangle not a square? These sorts of questions might sound funny, but they’re really important because if we want to spot a square every single time we see one, we need to know what makes it a square. And there are three ideas we can use to help us.

These are the words “always,” “sometimes,” and “never.” Let’s see how these words can help us. Our picture shows an orange square. Now, can we say squares are always orange? Remember, the word “always” means every single one. Of course not. We can have blue squares, pink squares, or even red spotty squares. Squares are not always orange; they’re sometimes orange. The color of a square isn’t what makes it a square. The same is true of the size of a shape. Squares aren’t always this size. They’re only sometimes this size. Sometimes they’re smaller; sometimes they’re larger. We can’t spot a square by its size.

I hear you say, “I think I’ve spotted something.” Every single one of these squares has got a side that goes across from left to right at the top, one that does the same at the bottom. And they all have two sides that go straight up and down. Squares are always in the same position. Not if we turn them. We can see that a shape’s color, its size, and the position that it’s in are not really important when it comes to spotting what shape they are. The really useful word that we need to think about here is the word “always.” When we use this word, we mean every single time. What makes this shape a square are the things that every single square has in common.

And with 2D shapes, we need to look at things like the number of straight sides that a shape has and the number of vertices or corners. This square has four straight sides. We can show this by putting a plastic counter on each one just so we don’t miss any out. One, two, three, four. Can we say all squares have four straight sides? Yes, we can. Not only that, but they’re all the same length, aren’t they? So another always statement, one of these things that makes a square a square is that all squares have equal sides.

What about the number of vertices that a square has? Let’s count the corners on our blue square. One, two, three, four. Can we say all squares have four vertices? Yes, we can. Every single square ever has always had four corners. Without four corners, it wouldn’t be a square. And this is where we can think about the idea “never.” We could use our all statements to write some never statements. If we know that all squares have four straight sides, then we can say squares never have any curved sides.

And if we know that all squares have four corners, we could say squares never have more than four corners. If we’re going to go shape spotting, we don’t want to be looking at the color or the size or the position of a shape. We need to look for the features that all shapes of that type have in common, things like the number of straight sides and the number of corners. Let’s try answering some questions now where we have to put into practice the ideas of always, sometimes, and never. Let’s go shape spotting.

Fill in the blanks in the following sentences about triangles. All triangles what. Have more than three sides, are yellow, or have three sides. But only some triangles what. Have three corners, are green, or have three straight sides.

This question is all about the 2D shape, the triangle. And we’re given some pictures to help us. We’re given two very short sentences to complete. Did you notice the main difference between them? There are two very small words, but they make a lot of difference. In the first sentence, it’s the word “all.” This means everything, doesn’t it, every single one. So to complete this sentence, we’re looking for a feature of triangles that every single triangle has. This is going to be one of the things that makes a triangle a triangle.

Now, the small word in our second sentence is the word “some.” This word is different because it means not all, part of the whole amount. And when we complete this sentence, we’re looking for a feature that not every triangle has in common, only some of them do. Let’s start with our first sentence then. All triangles what. Can we say that all the triangles in the picture and all the triangles we could ever draw have more than three sides? If we count the number of sides that our first triangle has, there are one, two, three.

We can use the picture to help us here. And we can say that all of the triangles in the picture do have three sides. And even if we were to draw some of our own, they would also have three sides. We can’t say all triangles have more than three sides, can we? We can’t even say some triangles have more than three sides. We’d have to say, no triangle ever has more than three sides.

Now, what about the color of these shapes? Can we say all triangles are yellow? Although one of our triangles in the picture is a yellowy-orange color, we know that triangles can be any color. They could be pink, green, or white, like in the picture. But they could also be blue stripy or shiny silver. I suppose we could say some triangles are yellow. The color of a triangle isn’t something that makes it a triangle. Now, we’re only left with one possible answer. All triangles have three sides. Well, we don’t need to think too much about this, do we? We’ve already talked about the fact that every single triangle has got three straight sides. We can say all triangles have three sides.

Now let’s think about our second sentence. But only some triangles what. Do only some triangles have three corners. Well, we can see on our first triangle in the picture that it does have three corners. In fact, so do all the others. This isn’t something that only some triangles have. This is something that’s true of every triangle. It’s one of those features that makes a triangle a triangle. We could actually use this phrase in our first sentence, “All triangles have three corners.” Let’s try our second phrase. Can we say only some triangles are green? Yes, we can, can’t we?

As we’ve said already, triangles can be any color. Of course, only some triangles are green, knowing the color of a shape doesn’t help us identify what sort of a shape it is at all. And let’s just check our last phrase. Only some triangles have three straight sides. Not at all. As we’ve found out already, all triangles have three straight sides. In this question, we’ve thought about the things that are always true of triangles and the things that are sometimes true. And this helped us complete the sentences. All triangles have three sides. But only some triangles are green.

Anthony has sorted these shapes into two groups, group one and group two. Why does this shape belong in group one? Because it is green, because it has more than four sides, or because it is a rectangle.

We can tell by reading this question that Anthony has done some shape sorting here. He’s had some 2D shapes, and he sorted them into two groups. Now, this question is really interesting because it gets us thinking about what different 2D shapes have in common. In particular, we’re thinking about the 2D shapes that are in group one because we’re given a picture of a shape and we’re asked, why does it belong in group one? Can you see it in group one? Looks like this shape here, doesn’t it? And why has Anthony decided to put this particular shape with all the others in group one?

Is it because it’s green? Well, you can understand why somebody might think this was the right answer. It is a green shape, and all the other shapes in group one are also green. So do you think the rule for putting a shape in group one is that they’re green? No, because if we look in group two, we can see a green circle and a green triangle. Just because some shapes are the same color doesn’t mean they’re the same type of shape at all. Anthony hasn’t sorted these shapes by color, has he?

Now, do you think this shape belongs in group one because it has more than four sides? Well, if we actually count the number of sides that this shape has, we can see that it has four sides, not more than four sides. So this statement isn’t true at all. Now, this is where the question gets interesting because if this statement said, because it has four sides, it still wouldn’t be the right answer. Can you see that one of the shapes in group two also has four sides?

Anthony hasn’t chosen to sort these shapes based on the number of sides that they have. This only leaves us with one possible answer. This shape belongs in group one because it’s a rectangle. And Anthony has sorted out all the rectangles and put them all together in group one. And if we look at all the shapes in group one, there are some features that they all have in common. These are the things that make them rectangles. Each one of them has four square corners. And they all have four straight sides. These are the things Anthony was looking for when he wanted to sort these shapes into group one, not the fact they were green. This shape belongs in group one because it is a rectangle.

There is a mystery shape in this bag. Which clue will not help you guess the name of the shape? It has five corners, it is green, or it has five straight sides. Based on these clues, what is the shape in the bag? Is it a square, a triangle, or a pentagon?

Are you feeling like a shape detective? Well, you’re going to need to be one with this question because we’re told we have a mystery shape in the bag. And like any detective, we’re given some clues to help us solve the problem. But not all of the three clues are useful. We’re asked, which clue will not help you guess the name of the shape? Now, all these clues are true about our shape, but not all of them are useful. The first clue talks about the number of corners that our shape has. The second clue talks about its color. And our third clue talks about the number of straight sides that it has. Which one of these clues isn’t very useful at all?

It’s the color, isn’t it? Knowing the color of a shape doesn’t help us tell what it is. Some circles are green, some triangles are green, any shape at all could be green. Knowing that the shape is green is not going to help us at all. If we want to be true shape detectives, we need to use clues like the number of corners that a shape has, and here we’re told that it has five corners, and also the number of straight sides that it has, and we’re told that it has five straight sides. In the second part of the question, we need to put these clues to the test.

Based on these clues, what is the shape in the bag? Is it a square, a triangle, or a pentagon? Now, one shape might jump out straightaway as being wrong. We can see straightaway that the triangle is the only shape that isn’t green. So we do know that the answer is not going to be the triangle. But it would be a shame if we cross the triangle off our list straightaway just because it was the wrong color. As we’ve said already, the color of a shape isn’t something we can rely on.

So let’s think of our two clues that really matter. It has five corners, and it has five straight sides. How many corners does a square have? One, two, three, four corners, not five. And we also know that a square has one, two, three, four straight sides, not five. The shape in the bag is not the square. As we’ve already said, we know that the shape isn’t the triangle cause it’s red. But let’s look at the more important clues. Triangles have three corners, not five, and three sides, not five.

This only leaves us with the pentagon. A pentagon, it’s a shape that has one, two, three, four, five corners. And we can count one, two, three, four, five straight sides. Of course, the pentagon is green as well. But it’s not this clue that helped us. As any good shape detective knows, we can tell a shape by the number of straight sides that it has and the number of corners or vertices that it has. The clue that did not help us guess the name of the shape was, it is green. So we used the remaining two clues, it has five corners and it has five straight sides, to help us identify the mystery shape as the pentagon.

What have we learned in this video? We’ve learned how to look carefully at 2D shapes to see what features a shape always has, sometimes has, or never has.

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