Lesson video

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Hello, and welcome to this lesson on similar triangles with me, Miss Oreyomi.

For today's lesson you'll be needing your pencil, your protractor, so you'll be needing this, you'll also be needing a ruler, a rubber, and, of course, you will be needing your book.

So, pause the video now if you need to go get this equipment, also, try to minimise distraction by putting your phone on silent, get it into a space where there's less distraction and being ready to learn, because today's lesson is so fun, as you'll be using this tool to draw triangles.

So, pause the video now and go and get your equipment, when you're ready, press play to begin the lesson.

You have four triangles on your screen and your job is to find the value of the missing angles in each triangle, and it's also very important that you explain your reasoning clearly.

So, pause the video now and attempt these four tasks, once you're done, press play to come back to find out the answers.

Okay, I hope you found that task straightforward, we're just going to go through the answers very quickly.

So over here, I know that the sum of angles in a triangle add up to 180 degrees, so my a must be 130 degrees.

Here, this is an isosceles triangle, so therefore this angle here is 34 degrees, and 34 plus 34 is 68, so 180 takeaway 68 is b, which is 112 degrees.

If I move on to this, this we've already been given this angle as 112 degrees, well, 180 takeaway 112 is 64, but because it's an isosceles triangle I'm going to split it between my two base angles, so this will be 34 degrees and my d would be 34 degrees too.

Well here, again, the sum of angles in a triangle add up to 180, I have 150 at the moment, so therefore e must be 30 degrees.

So I hope you got that, if you didn't just check your work and try to see where you went wrong and correct yourself as well.

Whilst you were doing that task.

I wonder if you noticed something about these triangles, I wonder if you thought, hmm, I can see some things are the same, whereas I can see some things are different, because that links in very nicely to what we're doing in today's lesson, did you notice similarities and differences? Well, I noticed that these two angles here have the same, they have the same interior angles, however, this triangle is smaller than this triangle.

And also the same for this, these two have the same interior angles, however, the position has been different, so these two are the same, whereas the two base angles have been put in different positions, and that links into similar triangles.

So our connect task, two students were asked to draw a triangle where two of the angles were 70 degrees and 55 degrees.

So firstly, what's the first thought you're thinking? I have 70 degrees and, I've got one angle is 70 degrees and another angle is 55 degrees, so my third angle must be? Well, it must be 55 degrees as well, because I've got 70 and 55, and I need to add something that would give me 180, and therefore my missing angle is 55 degrees, so what type of triangle are these students trying to draw? Well yes, they're trying to draw an isosceles triangle.

First student started by drawing a base of six centimetre, so she started by drawing a base of six centimetre and then she's gone ahead and measured 70 degrees using her protractor, and then our second student started by drawing a base of three centimetre and then he's measured 55 degrees first.

How can these students complete their drawing? So what can our first student do over here to complete her drawing and what can our second student do over here to complete his drawing? Well, she could put her protractor over here and measure 55 degrees, and he could place the protractor over here and measure 70 degrees.

We are going to have a go at doing this.

Can you, in your book, draw a triangle of 70 degrees and 55 degrees? If you're confident using a protractor, you can pause the video now and try to draw a triangle where the base is 70 degrees, and where two of the angles in your triangle are 70 degrees and 55 degrees.

If you're not so sure how to do this, then carry on watching the video and I'll be providing a tutorial video of how to use a protractor to draw a triangle.

This is hurting.

Okay, before we proceed with you drawing your triangles, I thought a video and me explaining what is happening in the video would give you the support and the foundation you need to be able to use your own protractor.

So before we start I'm going to, is I'm going to talk over in the videos but before we start, let's just do some labelling very quickly.

This part of your protractor is called the centre, so this is called the centre, the zero going from the outside is called the outer scale because it's reading from the outside.

If you see here, we also have a zero and this is the inner scale, so outer scale, inner scale, and then this straight line here is called the base line, so you're going to be needing this, you'll be needing to know this for this task, okay? Let's start with the video, so I'm going to press play.

If at any point you don't quite understand what I'm doing, please pause the video and rewind to watch again.

So first thing I'm doing is I am drawing my base line, or I'm drawing my base length for my triangle and I have chosen five centimetre, because I wasn't given a base line, I chose any value and I chose five centimetre.

Now, I have taken my protractor, I have put, so that's the outer scale, that's the inner scale, and that's the centre, so I'm taking my centre now and putting it on my line.

Now, because the base line of my protractor is on the straight line that I've drawn to this way, I am reading from the outer scale, so I'm always reading from zero.

My zero is on the outer scale on this side, so I am reading from zero, and I'm looking for 70 degrees.

I have found 70 degrees so I am marking that on my book.

I am then going to draw a line of any length, just so I've marked that this is my 70 degree angle.

I like to measure again just to make sure I haven't made a mistake, and yes, it is 70 degrees, so I am going to mark that in my book.

Okay, notice how my centre is now at the other end of my line, my center's now at the other end of my line, and my base line for my protractor is now on this side of the line that I've drawn.

So previously my base line was here, so I was reading the outer value, now my base line is this way, so I am reading, I have to read the inner value because that is where my zero is starting from on this line, okay? So I am now looking for 55 degrees, I have found 55 degrees so I am going to mark it on my book.

I am going to take my ruler and connect it up, notice that I have excess lines at the top but I'm not going to rub those out because, well, it just shows that I have drawn this using a protractor.

So that's a 70 degrees, I am measuring making sure it is roughly around 55, it is 55 degrees, and then the top one, I am just going to measure to make sure that is roughly around 55 degrees, and it is roughly, it's about 57, if your angle is two degrees more or two degrees less, that is fine, so I'm going to write it's approximately 55 degree.

Because this is a new skill to learn, I am going to do another example, so if you need to play this at a slower rate then please do so, okay? Now this time around, I have chosen my base length for my triangle to be four centimetre, so I'm going to label that as four centimetre.

Then again, I'm going to take my protractor, put the centre of my protector at the end of one line and read from the zero value, this time around, I'm starting with 55 degrees.

I'm going to take my ruler and connect it up from where I put the centre of my protractor.

Going to take my protractor, or just measure it again, like I said, I like to measure it, make sure that I've got in roughly the right value.

Now, I'm going to put the centre of my protractor and read the inner value this time for 70 degrees.

Again, I'm going to connect it up, and measure it again, just to make sure that I have the, I have drawn the correct angle, and that should also be roughly around 55 degrees.

You can use this video to help you, using your protractor and your ruler, can you draw a triangle where two of the angles are 70 degrees and 55 degrees? So you can choose your base length for your triangle to be of any length, your choice, so pause the video now, attempt this and then come back when you're ready and we can go through what you've drawn as well.

Okay, I hope you managed to construct your own triangle.

We're now going to compare what is the same and different about the triangles our students on our screen have drawn and the triangle that you managed to draw as well.

So if we link this to our try this task, well, we can see that this is 55 degrees and this is 70 degrees, the same as this triangle here is 55 degrees for this student and it's 70 degrees for this student.

If we complete, if we fill in this missing angle, this is going to also be 55 degrees, just as this is going to be 55 degrees.

So, for both students, we can say the interior angles are the same, exactly, the interior angles for both triangles are the same.

Well, what is different? Well, the lengths are different, this is three centimetre and this is six centimetre, so we could say that these are different lengths.

What else could we say? Both isosceles triangle? Yes, they are, they're different orientation though, so one, the base length of the triangle is at the bottom whereas the base line of the triangle is at the top for this smaller triangle over here.

And we can say one has sides that are twice as long as the other, so this is six centimetre, this is three centimetre, this is 3.

4 centimetre, this is 6.

8 centimetre, and this is three centimetre again, and this is six centimetre.

So, we could say these two triangles are similar, they are similar because they have the same interior angle, and they're also, there's a link between the lengths of their sides.

Can you draw different triangles where at least one of the sides is 10 centimetre long? So, using your ruler, you're going to measure one of the sides of the triangle to be 10 centimetre long, and then you're going to measure two for the first one where two of the angles are 60 degrees, so you want to draw a triangle where at least one of the sides is 10 centimetre long and where two of the angles are 60 degrees.

Secondly, how many different triangles can you draw where one of the side length is 10 centimetre, and for the second one, two of the angles are 20 degrees, okay, so you want two angles to be 20 degrees.

And then for C, you want one angle to be 20 degree, the other angle to be 60 degree, and I've given you a hint here, work out the third angle.

So just to recap your instruction, when I tell you to, you're going to pause your screen, you're going to draw, A, you're going to draw a triangle where at least one of the side length is 10 centimetre and two of your angles in your triangle for A are 60 degrees.

For B, you're going to draw a triangle where at least one of the side length is 10 centimetre and two of your angles are 20 degrees.

For C, you are going to draw a triangle where again, you have one side that is 10 centimetre, one angle is 20 degrees, another angle is 60 degrees, and what is going to be your third angle? Pause your screen now and attempt this, and when you finish, come back and we can discuss some of the possible triangles that you came up with.

How did you get on, did you manage to draw your different triangles? We're going to go over the possibilities of what you could have drawn.

So for the first one, one of the side length is 10 centimetre, well, it is an equilateral triangle, isn't it, because if I've got two angles as 60 degrees, well, the third angle has got to be 60 degrees, so there's only one way I could have drawn this triangle because however way I draw it, all my angles will always be 60 degrees, and because it's an equilateral triangle, my side lengths are the same.

Now for this one, where two angles are 20 degrees and the side length is 10 centimetre, I could have started by drawing my side length to be here, so if I'd drawn my side length here of 10 centimetre, then this is one possible way I could have drawn my triangle.

Another way would be to draw my base length to be 10 centimetre, if I had done that, this would be a way I could have drawn my triangle.

Notice how, when my side length is opposite a smaller angle, my triangle is bigger.

There are three ways I could have drawn the last one.

I could have started from here, drawing this side as 10 centimetre first, then measuring my 20 degrees, my 60 degrees, and therefore my last angle would be 100 degrees.

I could have drawn my base length, I could have drawn my base length to be here as 10 centimetre, and the last possible way to have done it would be to draw my base length here.

We're now moving on to our independent task, I want you to pause the video now and attempt all the questions on your worksheet.

It's probably better if you look at the questions on the worksheet rather than on the video, and attempt the questions and once you're done, come back and we'll go through the answers together.

Okay, let's go over our answers together.

So we've got 180, because this is an isoceles triangle, 180 take away 54 is 126, so we divide that by two, I get 63 degrees here and I get 63 degrees here.

90 plus 27, that takes us to 117, so a will be 63 degrees.

Okay, for the third one I've already written 63 degrees so we have 63 degrees because base line, isosceles triangle have equal angle, so therefore this would be 54 degrees, and d here would be 90 degrees.

For the next one I have drawn this and I've inserted the picture so checking that yours looks similar to this.

Okay, and then for c and d, I started by drawing a base length for my triangle of seven centimetre for each, and then I measured, well, I didn't need to measure the right angle for this one because it just came up to a straight line.

Okay, now for 3, I started by drawing a base line at the bottom here, and then I thought I would change things up a bit and then I drew the base line over here, I drew my 3.

5 centimetre over here.

Checking your work, making sure they have drawn two different angles of interior angles of 35 degrees, 45 degrees and 100 degrees for both.

Okay, let's move on to our explore task.

Your job is to draw an accurate sketch of this triangle and then draw three different isosceles triangle that have at least one angle that is 40 degrees, and at least one side that is eight centimetre long.

So draw three different isosceles triangle that have at least one angle that is 90 degree and at least one side that is eight centimetre long.

So pause your screen now, I'm not going to provide you with support this time around because I think, I believe, that you should know how to do this, so pause your screen now, attempt this, and then when you finish, come back and we'll go over the answer.

Okay, how did you get on with yours? Well for this one, we were told that our triangle must have at least one angle that is 40 degrees.

Well, I've got one angle that's 40 degrees and then my bottom angles are 70 degrees each, so that's one way of doing that.

And then another way of doing it is, my base angle are 40 degrees, both 40 degrees, and then I've got 100 degrees at the top as well, and then I've got two lengths here of eight centimetre.

Over here I've got my base length of eight centimetre, and then again, the same as this, this is 40 degrees and this is 40 degrees, but this is 100 degrees.

Notice how in this one, my two lengths here are equal, whereas here this would be eight centimetre, and then this length here would be equal to this length here.

Did you draw the same ones as I did on the board? Okay, we have now reached the end of today's lesson and a very big well done for completing the task, you know, learning how to use a protractor, and again, keep practising.

Before you go though, show off your knowledge by completing the quiz, so just ensure that you complete the quiz to consolidate your knowledge and just to show yourself how much you've learned from today's lesson.

And I will see you at the next lesson.