Lesson video

Hello and welcome to today's lesson on comparing quadrilaterals with me Ms. Oreyomi You will be needing a paper, a pen, and a pencil in today's lesson.

I would recommend that you actually get a physical paper as that would really help with what we're doing today.

So if you need to pause the video now to go get your equipment and to minimise distractions, when you're ready come back and press PLAY and we can resume with the lesson.

Okay in this lesson, you will be able to compare the symmetry, side length, number of parallel sides, and angles in a quadrilateral.

So your first task is to draw this table out in your book.

Over here you have the diagram, if you don't want to draw the diagram, you don't have to draw the diagram, but it would be helpful if you actually draw out the main column, the lines of symmetry column, pairs of parallel sides column, and angle properties column as well.

So write the name of the shape, write what you think the number of lines of symmetries are, pairs of parallel sides, , and angle properties.

So pause the video now and attempt this task, and then once you're done, press PLAY to resume.

Okay, hopefully you have written a square for the first one, it's got 4 lines of symmetry, horizontally, horizo-, horizontally, vertically, and the diagonals as well.

2 pairs of parallel sides.

That's one pair and that's another pair of parallel sides.

And all the angles are 90 degrees, cause this is a right angle on each corner, so we got 90 degrees each.

This is a rectangle, it only has 2 lines of symmetry.

So it's got vertically and horizontally.

If you need to prove that get a, a piece of paper, make it into a rectangle and see if you fold it diagonally will it give you a line of symmetry and your answer should be, nope.

It's got 2 pairs of parallel sides, again up and the sides, and again each angle in a rectangle is 90 degrees.

A parallelogram, your third shape's a parallelogram.

It has no line of symmetry.

Again, it has 2 parallel sides and 2 pairs of equal angle.

So A and A are the same and B and B are the same.

This shape here is called a Trapezium.

Again, because it's an irregular trapezium it has no lines of symmetry and has 1 parallel sides over here.

It doesn't always have equal angles.

This shape here is a kite.

It has 1 line of symmetry going from the top here to the bottom over here.

And it has no parallel sides because if you remember parallel sides mean the lines that will never touch.

But this kite has no pair of parallel um sides and it has one pair of equal angle.

So A and A are equal.

At the bottom of our table we have a Rhombus.

It's got 2 lines of symmetry, 2 pairs of parallel sides are up there and the sides there as well, and it has 2 pairs of equal angles.

If you did not get this correctly, I would, I want you to pause your video and actually get this information down in your book cause it will prove very, very essential in the other tasks we do this lesson.

So pause the video now if you have to and just get this information down in your book.

Okay.

Previously I had mentioned a trapezium and I wasn't quite specific with the trapezium that I was talking about.

This slide I am talking about an isosceles trapezium.

If we think about an isosceles triangle, what are some of the properties of an isosceles triangle? It's got one line of symmetry, it's got 2 equal angles, right? Well that is very the same with an isosceles triangle.

It has one pair of parallel sides at the top line and the bottom line are parallel.

It has one line of symmetry along the middle here and it has two pairs of equal angle.

So this angle is equal to this angle and these two bottom angles are equal.

So again, we're going to be using this information for the rest of our lesson.

We are told to try to draw quadrilaterals on a square piece of paper that has exactly one line of symmetry.

Now just to remind ourselves, quadrilaterals are four-sided shape.

We want a four-sided shape that has exactly one line of symmetry.

Well what shape can we draw that has one line of symmetry? I'm thinking I could draw an isosceles trapezium.

So I've got that there, over there.

You would see that drawing on a square piece of paper really helps as you can see the line of symmetry very easily.

So this in the middle, would be my line of symmetry.

So I have ticked this one here.

I want to draw a quadrilateral that has two pairs of equal angle.

Well, I can draw a parallelogram.

A parallelogram has two pairs, of equal angle.

So this is the same as this, that is not a right angle.

This here, this angle is the same as this angle.

And this angle here, just going to shade it in, is the same as this angle over here.

And I'm just going to put this to show my parallel sides.

Great.

So I have drawn a quadrilateral that has two pairs of equal angles.

Now I want to draw exactly one, I want to draw a quadrilateral that has exactly one pair of parallel sides.

What quadrilateral has exactly one pair of parallel side? Well I can think back to my Try This task and to previous activity, and I know that a a trapezium has exactly one pair of parallel sides.

So I'm just going to draw that here.

Like so.

Right, this is a neater version of what I've just explained to you.

Here we have our kite, it has one line of symmetry going through it.

We could also have a delta, and this also has one line of symmetry.

A quadrilateral with one line of symmetry and the example I gave you an isosceles trapezium.

Okay, a quadrilateral with one pair of parallel sides.

Examples are trapezium and then a quadrilateral with two pairs of equal angle.

Well as we said these two angles are the same and our parallelogram opposite angles are the same.

The same with our rhombus, opposite angles are the same.

Very soon you're going to start your independent task.

Before you do there's a question that you may get confused about so I'm just going to explain what that question is asking you to do.

So your last question is to draw a sketch of quadrilaterals for each of the numbered section in the Venn diagram.

The Venn diagram, this side means you want a quadrilateral that has four sides of equal length.

So here I could draw a square, cause I know that has four sides of equal length.

And then number two here it's saying I want you to draw a quadrilateral that has four sides of equal length and four equal angles as well.

So that would be number two.

Number three would be a quadrilateral that has four equal angles.

And then number four would be any quadrilateral that doesn't have equal- four sides of equal length that doesn't have four equal angles.

Okay.

Now pause your screen.

Attempt all the questions on your independent task.

And then when you're finished come back and resume the video and we'll go over the answers together.

Okay let's go over the question one together.

Ali is drawing quadrilaterals using their lines of symmetry.

Use square paper to copy and complete his drawings, then name the quadrilateral.

Usually if I don't have square paper, I would trace over my screen to to get a picture, to get a better, to get an accurate drawing of my diagram.

So the first one is an isosceles trapezium because, well, connect and then we'll upload this would give me that.

So that's an isosceles trapezium.

I'm just going to do one more, this is going to be a square.

Well because it is reflected over my line of symmetry and it gives me a square.

The same goes for that one as well.

This H is a scalene quadrilateral that means any quadrilateral that is not that doesn't have equal sides, that doesn't have equal length.

Because there is no line of symmetry, it mean all the lengths are different.

So for example, I could do something like this.

Okay, it's a quadrilateral because it has fours sides.

But I don't have a line of symmetry because I can't fold it in half and it would give me the exact same shape if I do.

Okay, second question.

Krish is making quadrilaterals by touching the sides of two identical isosceles triangles below.

What quadrilaterals can she make? Well, if she touches the side this is going to be a very, very, very very, rough sketch.

But I've got that base touching here, and then I've got my two other trian- my two other sides and I could create a rhombus from this, cause all my sides will be the same.

So that's the one way I could create a rhombus.

And if I want to draw a delta, I could go like that.

So that's my first triangle, and then connect my second triangle like so.

Hopefully yours is a lot neater than mine, but use a straight-line, using a ruler rather and a pencil you could see how you could connect the two triangles together to get a delta.

Okay looking at the last question then, draw a sketch of a quadrilateral for each of the numbered sections in the Venn Diagram.

So over here I have written what shape could fit into each of these statements.

So the first one is: four sides of equal length.

Well we know that the rhombus has four side of equal length, so that would go in section 1.

Number 2, four sides of equal length and four equal angles, would definitely be a square.

Number 3, only four equal angles, and that is a rectangle.

Number 4 is a kite, because a kite or a parallelogram does not have four equal angles or four equal sides, four sides of equal length.

The next one we want a shape that has four sides of equal length, and that is a square.

So a square would go in section 1.

Number 2 we want a shape that has four sides of equal length and two sets of parallel sides, and that is either a square or a rhombus.

3, we want two, a shape with two sets of parallel sides, and that's a rectangle or a parallelogram.

And number 4, delta, kite, isosceles trapezium they don't have two sets of parallel sides nor do they have four sides of equal length.

The last one then, we want a shape with one line of symmetry and that is a kite or a delta, so a kite or a delta would go in section 1 here.

Number 2, we want one line of symmetry, a shape with one line of symmetry and one pair of parallel sides, and that is our isosceles triangle.

And number 3 we want a shape with just one pair of parallel sides, and that again is an isosceles triangle.

And number 4, a shape with, that doesn't have one pair of parallel sides and doesn't have one line of symmetry is a square or a rectangle.

Right, moving on to explore tasks, I am going to read it out: It is possible to make a hexagon by overlapping two identical equilateral triangles.

So these are my two identical equilateral triangles, I overlapped them and then if I delete the excess bit over there, I end up with this.

And it's a hexagon because it has six sides.

So 1, 2, 3, 4, 5, 6.

Notice it doesn't say a regular hexagon.

So that means my hexagon could have taken any shape whatsoever as long as it has six sides.

What other polygons can be formed by combining the two triangles? What other polygons can you form if you combine two equilateral triangles together? And just to say, a polygon is any two side, any 2-D shape, with straight side.

So it could be 15 sides, it could be 10 sides, as long as the sides are straight like the example given here, then it is a polygon.

So pause your screen now and I want you to come up with many different polygons as you can make using two triangles.

If you are struggling with this task, then carry on watching the video and I will provide you with further help.

Okay for support, I have my two triangles over here and I want to see what quadrilaterals I can make, what polygon rather, I can make by joining them together.

Well, I can make a quadrilateral if I join the sides of my triangle together and then if I delete this collectant side I would have a quadrilateral.

So, your turn now if you put the triangle in different ways whether they're overlapped or whether it's like this, what polygons can you make from this? Pause the video now and attempt the task.

Okay these are some polygons you could've made by combining two triangles.

Did you come up with some on the board? Were yours different? Were they the same? We have now reached the end of today's lesson.

A very big well done for sticking through with it, and for completing the task as well.

And I hope I will see you at the next lesson.