A quadrilateral with four equal sides and four right angles.

A quadrilateral with only one pair of parallel sides.

A quadrilateral with two pairs of equal sides and two pairs of equal angles

Select the correct description of a trapezium.

The interior angles in a quadrilateral add up to:

If a parallelogram has a perimeter of 6cm, what are the lengths of the sides?

Compare and classify quadrilaterals

Key Stage 2

Maths

Missing angles and lengths

What do the angles in a triangle add up to?

What type of triangle is shown in the picture below?

Is this statement always true, sometimes true or never true.

﻿Welcome to our third lesson in this unit, finding missing angles and lengths. Today we're going to be comparing and classifying quadrilaterals. First of all, make sure that you have everything you need. Just a pencil and piece of paper today. Here's the agenda for the lesson. We'll be comparing and classifying quadrilaterals, starting with a quiz to test your knowledge from the previous lesson. Then we'll look at classifying quadrilaterals before looking at angles and quadrilaterals. Then you'll move on to some independent learning before doing a final quiz to test what you've learned in today's lesson. So let's start with the quiz, pause the video and complete the quiz. Restart once you've finished. Great work, now here's your do now, who you agree with and why? The first person thinks that all of the shapes are quadrilaterals because they all have four sides. The second person thinks that half of the shapes are quadrilaterals and half are not. Who do you agree with? Pause the video and make some notes. Sides, that there's something very important to remember is that quadrilaterals have four straight sides and four internal angles. So when I look at these shapes, I can see that this shape and this one, and this one have straight sides, but here we have a curved side and so on these ones as well. Therefore the second person is right. Half of the shapes are quadrilateral, because they have straight sides. Now we've got some new vocabulary. So we're going to be looking today at polygons. A polygon is a flat two dimensional shape with straight sides that is fully closed. So all of the sides join up together. Remember the sides must be straight. Polygons can have any number of sides. But a shape with curved sides is not a polygon. So here's our first bit of vocab. A regular polygon is a polygon in which all sides and all internal angles are equal. So here we have a pentagon, which is a five-sided shape that has equal sides, therefore it is a regular pentagon. Then we have irregular shapes. That's a polygon where not all of the sides and internal angles are equal. Here we have an octagon which has eight sides, and you can see that these sides are equal lengths and these sides are equal length, but they're not all equal. Therefore it's an irregular octagon. The next word is parallel. And here's an image of parallel lines. These are lines that will never intersect, which means to join. And they are equidistant, which means that every, each point of the lines is the same distance apart. They are equidistant, they're an equal distance apart. And I always remember what parallel means because inside the word parallel, there's a pair of parallel lines. The last, perpendicular, this is when two lines intersect or join at a 90 degree angle. And here is your image to represent that word. So you may want to pause the video and make some notes on these words, we'll be using them throughout the lesson. Now our first shape that we're going to identify is parallelograms and if you think back to our vocabulary, this must have something to do with those parallel lines, lines that are equidistant, they're the same distance apart. We're going to be looking at these shapes here and identifying which are parallelograms and which are not. So a parallelogram is a polygon that has two pairs of parallel lines, and it has two pairs of equal angles. And squares and rectangles are also parallelograms. So I'll start with A, I can see that A has got a pair of parallel lines, and we mark parallel lines with an arrow like this. These lines, no matter where you get to on, each point on these two lines, they are an equal distance apart, therefore they are parallel. However, the other two lines are not parallel. So this is not a parallelogram. In B, although this is an orientation that you may not normally be used to seeing. This is a parallelogram because it has got pair of parallel lines here and a pair of parallel lines here. Shape B, this is important for later on in the lesson, is also called a rhombus. It's a parallelogram, which has all equal sides. That's a rhombus. So it has equal sides but it also has two pairs of parallel lines. Let's look at one more together before you look at the rest by yourself. Shape C, I can already see that it's a square, and parallelograms include squares because these lines are parallel and these lines are parallel. So that is a parallelogram, okay? And remember we'll go back to this one. A rhombus is also a parallelogram. Now pause the video and have a look at the rest of the shapes. Which of them are parallelograms and which are not? So shape D is a parallelogram because these two lines are parallel, they are equidistant. And so are these. And this is actually a rectangle as well. Remember that rectangles are parallelograms. So that's a yes. E, well I can see a pair of parallel lines here, but the other two are not equidistant, at the top they are closer together than they are at the bottom, so that's not a parallelogram. F is, the top and bottom line are parallel. And the side two lines are parallel, so that's a yes. G is also a parallelogram. And you will usually see these signs marked on the shapes so that you can judge it yourself. And then H has got a pair of parallel lines here, although its difficult to see, sometimes you have to turn your page, but the other ones they're much closer there than they are up there, so that's not. I has got no parallel lines and neither has J. So remember, a parallelogram has two pairs of parallel lines and two pairs of equal angles. Let's look at trapezia. So trapezia is the plural of trapezium. So you have one trapezium and lots of trapezia. Trapezium has one pair of parallel lines. Now I remember from the previous slide that there were a few shapes on here with one pair of parallel lines. The first one was A, so I'll mark that on there. That's a pair of parallel lines, but the other two are not. So this is a trapezium. Now pause the video and figure out which of the others are trapezia. So I won't go through all of them because we remember from the previous slide that B, C and D were all parallel. E is a trapezium because it has one pair of parallel lines. The other two are not. So that is a trapezium. F was a parallelogram, so was G and H is a trapezium. And like I said before it's easier if you turn your paper around. So if I turn my paper, you can now see what each would look like if it was standing on its base. And you can see that these two lines, if I carry this one along like that, they are parallel lines, so that is a trapezium. And we said, I and J have no pairs of parallel lines, so they are not. Now other quadrilaterals, I and J we're the only two shapes that we didn't identify. I is a quadrilateral because it has four sides, but it has no parallel lines, so it's not a trapezium or a parallelogram. It's got two pairs of equal sides that are of equal length and they're connected at a point. And you may have seen this in a different orientation, looking like this. I is a kite. And J, this is a quadrilateral that has got two pairs of equal length sides. So those two are equal and these two are equal. It also has one internal reflex angle. This shape is called a Delta and it looks a bit like an arrow head. Now it's your turn, pause the video and match the shapes to their name. And we remember that parallelograms have two pairs of parallel lines and include squares and rectangles. So that B is a parallelogram. B, G, and H. Remember that this is called a rhombus, but it's still a type of parallelogram, it has all equal sides. I keep coming back to that one, because you're going to need to use that later. Trapezia have one pair of parallel lines. So that's C, and it's always helpful to mark them on there. A, E, and it's sometimes easy to turn your piece of paper or if you know you're doing this on the computer or the iPad, so to turn that screen around. And J. And then your other quadrilaterals were F. F was your Delta. And I, I was your kite. Now let's look at the angles in a quadrilateral. So here we have a square. Think about what you know about the angles in a square. Think about how I have drawn those on. So they're all right angles. And you know that a right angle has a value of 90 degrees. So in a square there are four 90 degree angles. So a square, the interior angles are four lots of 90 degrees. So either 90 plus 90 plus 90 plus 90 or four times 90, that gives us the interior angles in a square. If I knew that four times nine is 36, then I know that four times 90 is 360. So the interior angles in a square add up to 360 degrees. I wonder if that's the same for all quadrilaterals. Let's have a look. In a rectangle, it's the same as a square. We've got four lots of 90 degrees. And we know that four times 90 is equal to 360 degrees. So the angles in a rectangle, sorry, also add up to 360 degrees. Now, it's your turn, you're going to add up the interior angles in the quadrilaterals below and see what you notice. Pause the video while you do so. So that's absolutely right. All of the angles inside these quadrilaterals added up to 360 degrees. Therefore we can generalise that the internal angles in a quadrilateral always add up to 360 degrees. Now, one more thing to remember, this is an important piece of information, in a parallelogram opposite angles are equal. So you can see that this angle is opposite, mark it on that angle is opposite to this angle, and they are equal, they're the same. And this angle is opposite this angle, and they're the same. And if you add them all together, they would total 360 degrees. It's the same for a rhombus, which is a type of parallelogram, opposite angles are equal. A is equal to C and B is equal to D. I've told you this for a reason, which will help you in your independent test. So you may want to pause the video and make a quick note of that. Now it's time for some learning. Pause the video and complete the task and restart once you're finished so that we can go through the answers together. Great work, let's look at question one. Here you were given a square that was represented by being divided diagonally in half. What did this help you to reason about the sum of its internal angles? Well, we can see from this, that a square is made up of two triangles. We know that the angles in a triangle add up to 180 degree. And we know that 180 multiplied by two is equal to 360 degrees. So the angles in a square equal 360 degrees. And this helps us to see that that's two triangles, two lots of 180. And it's important for us to link these ideas together. Question two, you were working through a flow chart. So I asked you to start with the top shape and work your way down. So starting with the trapezium, is there at least one pair of parallel sides? Yes. Are all of the sides the same length? No. And are there two pairs of parallel sides in a trapezium? No. So your trapezium should go in here. Okay. On a parallelogram, remember two pairs of parallel sides and two pairs of equal sides. Is there at least one pair of parallel sides? Yes. Are all of the sides the same length? No, not always. Are there two pairs of parallel lines? Yes. Are there any right angles? No. So our parallelogram goes in here. And you have to excuse my handwriting. There we go. Now onto our rectangle. And as you did this you may have found it helpful to draw as well. Are there at least one pair of parallel sides? Yes. Are the sides the same length? No. Are there two pairs of parallel sides? Yes. And are there any right angles? Yes. So our rectangle goes in here. And then on to the kite, remember the kite had two pairs of equal sides but no parallel lines. The kite, are there at least one pair of parallel lines? No. Are there two pairs of sides of equal length? Yes. So our kite goes there. Onto the square. Is there at least one pair of parallel sides? Yes. Are all the sides the same length? Yes. Are there any right angles? Yes. Our square must go here. The rhombus, I kept going on about that earlier, let's see where this goes. Is there at least one pair of parallel sides? Yes. Are all the sides the same length? Yes. Are there any right tangles? No. Rhombus. So we've got one space left, but let's just check. So quadrilateral, no special properties, in my mind, I'm thinking of the Delta. Is there at least one pair of parallel sides? No. And other two pairs of sides of equal length? Well, actually there are in a Delta, so we think of a different quadrilateral that is an irregular quadrilateral. It would have no pairs of sides of equal lengths. So that is your last one. Quadrilateral with nothing special about it. No special properties. Great work, onto question three. So each of the quadrilaterals has a perimeter of 16 centimetres. Remember that's the distance around all of the sides of the shape. Complete the table to show the possible length of each side. So remember these are all quadrilaterals. So they've all got four sides. That's why we have four columns. In a square, they had to be equal. So they had to be four, four, four, and four. And I'm actually going to go down and do the same for my rhombus because they all had equal sides. So they must be four as well. For the rectangle, you've got some combinations, you needed to have two sides the same length, and then another two sides of the same length, but they weren't equals, they're not squares. So you could have had two, two, six and six. Or you could have had some different combinations. Let's look at the parallelogram. The same as the rectangle it's got two pairs of equal sides. You could have had three, three, five, five. And the kite, again, two pairs of equal sides. You could have had one, one seven, seven. So these could be in any order here for the rectangle, the parallelogram and the kite. You could have had any of these three, but they could be in any place. And the trapezium, you can have any combination adding up to 16, because the sides don't need to be equal length. As long as the total was 16. Question four, you're asked to name the shapes and list their properties. So the first one was a square and you may have written something like, it has four equal sides. It has equal angles that are right angles. And you could have maybe also said, it's a type of parallelogram. The second one is a trapezium, with one pair of parallel sides. And the third one is also a trapezium. In question five, you were to use your knowledge of quadrilaterals to find the value of the missing angles in the shapes where you could see that these two are right angles, so you know that A and B are both 90 degrees. You may have also noticed that this is a trapezium. And if I added 180, 90, and 90, then my total of the internal angles is 360 degrees. My second shape is a rhombus. Remember that the opposite angles in a rhombus are equal. So this angle is equal to this angle. So C is 80 degrees. This angle is equal to this angle. So D is a hundred degrees. And if you add 100 plus 80 plus 100 plus 80, your internal angles total 360 degrees. Okay, it's time for your final quiz. Pause the video and complete the quiz. Restart it once you're finished. Our next lesson, we'll be finding the value of missing angles in triangles. I'll see you then.

Compare and classify quadrilaterals

Compare and classify quadrilaterals

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UnitMaths / Missing angles and lengths

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