Complete the sentence: We can draw different triangles that have the same ______ angles using a ruler and a ________.

What is the length of the missing side, k, on the larger triangle?

Yasmin and Xiavier are talking about constructing triangles. Yasmin says you need 2 sides lengths to be able to construct a triangle. Xiavier says you need a protractor to construct a triangle. Who is correct?

What equipment would you use to construct 95°, 6cm, 55° triangle correctly?

Both angles have the same interior angles of ____, _____ and _______

Similar Triangles Quiz

﻿Hello and welcome to this lesson on triangle construction with me Miss Priori. For today's lesson you will be needing your ruler, your protractor, your compass and your pencil as well, also a book. If you need to pause the video now to go and get these things, then please do so. Whilst you are doing that, ca you also put the phone on silent, so that you are not disturbed during the duration of this lesson and also try to get into a space where there is less noise and where you won't get easily distracted. So pause your video now and prepare yourself for this lesson, I want you ready, press play to resume with the lesson. Okay. You try this activity. Which of the following triangles can you draw by connecting the dots? So, I will suggest you trace over to your screen to get the circle on the dots, you can get a round object to draw circles around it and then put the dots around it as well so that you can form equilateral triangles. So which dots, would you connect, to be able to create Equilateral triangle and how many triangles can you create? Again, which dot would you join together to create Isosceles triangle and Scalene triangle? So pause the screen now, proceed with the task and then once you are ready, press play and we can go for the possible answers. Okay. These are some of the possible solutions that you could have come up with. So, for an Equilateral triangle, you could have connected dots like this, to form an Equilateral triangle also these dots here. The same for an Isosceles triangle and the same for a scalene triangle as well. So did you get those or did you get different ones? Okay. Lets think about the question or the statement on our screen right now. We are told to construct a triangle, with a side of six centimetre, right here. A side of eight centimetre and then an angle of 39 degrees. We are given two known angle, two known sides and one angle so we have, two known sides and one angle. This is different to previously when we had one known side and the angle. So now we have more information for which to construct our triangle. Here are four student constructed triangles, the same information as we had in the previous slide. One side of six centimetre another side of 8 centimetre and then an angle of 39 degrees. How can we describe how they have constructed their triangle? What is the same about what they have constructed and what is different about what they have constructed? So I want you to pause your screen out, take a moment or two, think about it, look at the four images on your screen what is the same about what they have done and what is different about what they have done? Take a moment now to think about this and then press resume when you are ready to carry on. Okay. If we look at triangle one, we could say that the students started by drawing the horizontal line first. We could say something like that and then they proceeded to draw, to measure rather the 39 degrees and then constructed a circle with radius of 6 centimetre. You would see that this triangle and this triangle are similar in the sense that they are sharing the same circle so there are two points of intersection here. There is one point here which is where our student drew her triangle and then there is another point of intersetion here which is where our student else drew a triangle. So triangle one and triangle two, they both started by drawing, a line of eight centimetres. The started by drawing the horizontal base length of eight centimetre and then their radius was six centimetre for their circle. If we move on to triangle 3, well again, our student started by drawing a baseline of eight centimetre. However, we don't see any construction lines here. Meaning you probably, you did not. Meaning you did not use a campus, you did note use a campus to construct this triangle, you simply used a ruler and a protractor. You drew baseline of eight centimetre, measured 39 degrees and then drew an exact line of six centimetre here. Where is for the last one, for number four, well our student was a little different. They drew a base length of six centimetre. I suppose the eight centimetre of the rest. They drew a base length of six centimetre and then their circle has a radius of one centimetre over here. Your task now is to construct a triangle with this information you have. One side six centimetre, one side eight centimetre and then an angle of 39 degrees. If you know how to use a protractor or a campus and a ruler to construct a triangle, then feel free to both there. However, on the next slide I will be showing you how you can construct this triangle and then you can proceed to construct your own. So pause the video now if you know what to do with your protractor, your campus and your ruler and construct this triangle or carry on watching if you need more support. Okay. The video shows me drawing or demonstrating how to construct. The four different ways of constructing this triangle with the given information that we have. So one side length of six centimetre another side of eight centimetre and then an angle of 39 degrees. So we are going to watch the video now pause it or go at your own pace if you think I'm going a bit too fast so do what works for you essentially. So for the first triangle I have started with a base of eight centimetres. So I have just drawn my eight centimetre line and then taking my protractor I am going to measure 39 degrees. So I'm using the inner scale this time so I'm measuring 39 degrees. I am going to draw a line for as long as I want because that is not going to be my six centimetre line so that is just a line of any length. Then I'm going to take my campus and measure six. The campus is behaving very funny. I'm going to measure six centimetre there and then draw a circle from the other end a circle of radius six centimetre. You would notice that my circle intersected the straight line at two points. So that would be, one way of constructing the triangle would be to draw the six centimetre line at one of the points where it intersects so that would be six centimetre and then the other way of constructing my circle would be to draw it at the second point where it intersected my line, my straight line so that is also another way of constructing this triangle. Remember we said the radius is always the same from the centre of the circle to any point of the circumference so that is also six metres, six centimetres rather. So first way of constructing the triangle and second way of constructing the triangle right there. Moving on to the third way I can construct the triangle, I don't need a campus for this one, I'm just going to draw an eight centimetre line. I should have labelled that I forgot to label it and then I'm going to measure 39 degrees over there. This time I'm ensuring that my line is six centimetre line, cause that is going to be my six centimetre line so right there exactly six centimetre and then I am just going to connect it to my base length. That's the third way I can construct this triangle. Moving on to the fourth way now this time now I am starting with a base of six centimetres so not eight this time, six centimetres so I have swapped my base length so its six centimetres again after I have labelled that line and I did not say yes a base length of six centimetre and then taking my protractor again I am going to measure 39 degrees which is right there. Again my line can be of any length because my base is six centimetre , I am measuring eight centimetre using my campus and my ruler. Get yourself a little comfort people this was not ideal so I'm measuring eight centimetres using my ruler and my campus and then I am going to draw a circle with a radius of eight centimetre. I should concede the initial line I drew did not touch my circle so I'm just going to extend that line. Now, my line should be bang on eight centimetres right there. Okay. Your turn now, can you construct one version of this triangle so take your protractor, take your campus construct a triangle with one side of six centimetre another side of eight centimetre with one angle of 39 degrees. Now you will see that there are two questions on your screen or rather two other things you have to do. One is to measure the other side of your triangle and the other is to measure the other angles in your triangle so I did not do any of those cause that is your job. Your job now is to construct this triangle with the given information on your screen and then measure the other sides of your triangle and measure the other angles in your triangle as well. To do this now, pause the screen and attempt this and then once you are ready we will resume with the lesson. Okay. I hope you were able to do that, I also measured the other lengths in my triangle and while depending on which one you drew, which triangle you constructed, the length will obviously be different and also your angles should have been close to 180 degrees. If its not 180 degrees it should be two degrees less or two degrees more than 180 degrees. Any more and you have probably done something wrong with your measurements so make sure check that. Okay. Your turn now, you are going to have lots, lots and lots of practise to use both your compass and your protractor. How many different triangles can you construct when: one side is of your triangle is nine centimetre, another side is six centimetre and you have an angle of 30 degrees? So how many different triangles can you construct, if you have this given information. What if you have this information. How many triangles can you construct if you have one side as eight centimetre another side is five centimetre and then an angle of 35 degrees? So again using the same technique I did, how many different triangles can you construct, given the second information on your screen? Then lastly how many different triangles can you construct, if you have two sides of seven centimetre and an angle of 42 degrees? What you should be doing now, experiment with this and then come back and we will talk through the different possibilities for each of the statement. If you had a go at that you would have noticed that you could have drawn four triangles, four different triangles for the first one. So you could have constructed four different triangles for the first one. So the first one is very similar for our discussion task but the second one you should have constructed two triangles and one of them is a right angle triangle, did you manage to get that? And for the last one, you should have constructed, two triangles because its an isosceles triangle and both of the triangles you should have constructed, are both isosceles triangle. So you have gotten that, if you haven't perhaps re-do it, using the video I put in the previous slides ensuring that you have measured your lines accurately as well. Okay. We are now moving on to our independent tasks so pause the idea now attempt every question on your screen and once you are ready come back and we will look for the answers together. Your explore task, I am going to read the statement out for you. A triangle has an interior angle of a degree, that means we don't know what the degree is, `its got an interior angle of a degree, a side of length three centimetre and another side of length four centimetre. Suggest a possible value for the degree so that there are four possible triangles you can draw and then suggest a value for the angle so that there are only two possible angles you can draw. So pause the video now and attempt this, what is the value of my angle so that I can draw four possible triangles with a side length of three centimetre and another side length of four centimetre and what should my angle be so that I can only draw two possible triangles. Pause this video now and attempt this task and then come back and you would see the answer on your screen when you come back. We have now reached the end of today's lesson, a very big well done for sticking right through to the end. It could come out as a more complicated skill, using a campus and a protractor but with more practise you will get better at it. Before you go, do complete the quiz so that you could tackle your knowledge and enjoy that you have actually, you know, learned things in this lesson and also show your friends or your family what your score on quizes were. So do complete the quiz and I will see you at the next lesson.

How many can be constructed with the following angle measures?100°, 40°, 40°

How many triangles can you draw with three side lengths of 4 cm, 5 cm and 10cm?

Complete the sentence about the image below: You can construct different triangles if you are given two _____ and one _____ angle.

For the image below, both of the triangles above have side lengths of ______ and 7cm and an interior angle of ______.

How many triangles can you draw with this information? One side of length 7 cm, one side of length 5cm and a 40° angles.

Triangle constructions Quiz

In this lesson, we will learn how to construct triangles given two sides and an angle.

Maths

Y7 Maths

Key Stage 3

Year 7

Miss

Triangle constructions

Constructing triangles and quadrilaterals

Geometry

THEME

UNIT

Exploring circles

Constructing triangles

Impossible triangles

Drawing Similar Triangles

Quadrilaterals in circles

Constructing quadrilaterals

Further constructions

Complete the sentence: The kite below has been formed by connecting the _____ of the circles with the __________ points.

The constructed quadrilateral below is a ....

This circle is drawn on a centimetre square grid. State the radius and diameter.

Lesson overview:Triangle constructions

Core Content

Constructing triangles and quadrilaterals: