Lesson video

Hello, I'm Mrs. Lashley, and I'm gonna be working with you throughout this lesson today.

By the end of this lesson, we're hoping that we can construct triangles by using intersecting circles accurately.

On the screen are some words that you will have used in your previous learning.

You may want to pause the video to refamiliarize yourself with those words so that you can follow along this lesson as well as possible.

So the lesson's got two learning cycles.

The first part is constructing a scalene triangle and the second part is constructing triangles with equal edges.

We're gonna make a start on constructing a scalene triangle.

In many parts of maths you might need a diagram and that diagram might be a shape.

And depending on the situation determines the level of accuracy or the detail that is needed.

It might be that you can just get away with doing a freehand sketch, so not using your geometry equipment just as pencil to just free hand out what the information you need.

There might be other situations though where a drawing will be better suited than a freehand sketch.

And so in this case you would be using a pencil and ruler.

But it wouldn't be done to scale or accurately.

Lastly, you might need to construct the shape.

And when you construct the shape, this is done accurately and you would be using your geometry equipment to do this construction.

Lucas is going to attempt to construct this triangle with a ruler and pencil.

And on the screen currently is a freehand sketch.

We've got a triangle, A, B, C, and we can see the length between AB and the length between BC.

That's all labelled on that freehand sketch.

But Lucas is going to construct it and he is gonna use a ruler and pencil.

So to start his construction, he first draws the edge AB using his ruler and pencil.

Remember it's a construction so he's gonna do this accurately.

He's going to make sure it's six centimetres.

So his line has been drawn, that is AB, and we know that that is being drawn to six centimetres.

Now he's looking to mark where the vertex C is located.

And we know from the freehand sketch that it needs to be nine centimetres from vertex B.

So using his ruler, he's put nine on vertex of B, and he is gonna mark C at the zero because then the distance between B and C is nine centimetres.

Now, he needs to see and check that if this is a construction that is done accurately, then the distance from A to C, that line segment AC, needs to be four centimetres, but it isn't.

You can see there on the ruler that it's about six centimetres from A.

So although he's drawn the edge length AB accurately using his ruler, he's marked C in a location that is nine centimetres from B, it isn't four centimetres from A.

And therefore, he hasn't managed to construct the triangle that he's trying to.

So he's gonna try again.

Mark in another position for C, nine centimetres from B.

But is this in the correct position? It's still isn't four centimetres.

It's closer to A or is moving in the right direction, but it still isn't four centimetres.

So he tries again.

It still isn't four centimetres.

And again, but it still isn't four.

4.

2 centimetres, but it isn't four.

And if it's a construction, it needs to be constructed accurately.

So Lucas continues with trying to find the location of C that is both nine centimetres from B and four centimetres from A, but none of the ones he has done so far are four centimetres from A.

There've been less than four centimetres, there've been more than four centimetres.

All of those are marked at nine centimetres from B, but they're not meeting the criteria of being four centimetres from A.

Finally, he has found the position of C, the third vertex to create the triangle.

And so he joins that vertex C to A and B, the other ends of the line segment to finish his construction and labelling it up with the dimensions on the triangle.

Lucas noticed the attempts for C have created an arc and you can see that there with the purple dashed arc, which Lucas has realised actually that makes so much sense because they were all a fixed distance from B.

They were all nine centimetres from B.

By drawing another circle at A that was four centimetres, you could find the location of C.

But Lucas reckons he can see that there's maybe somewhere else that C could have been.

Can you see where it is? So there are two points of intersection with the four centimetre circle and that nine centimetre arc.

And so both of these would be a construction of that triangle that Lucas was attempting to construct.

One is just a reflection of the other.

The line segments, AC, is still four centimetres, BC is still nine centimetres, and the original drawn line we're using the ruler, AB, is still six centimetres.

So constructing a triangle with a pencil and ruler is quite challenging to be accurate and to find that exact location of the third vertex.

And we just saw that actually, the circles was a way of finding the location in a much more efficient method.

So what equipment helps to draw circles? A pair of compasses.

So I'm hoping that you've got a pair of compasses alongside you that you can continue the rest of this lesson using.

A pair of compasses is the geometry equipment that you will use to accurately draw circles.

And we've just seen that circles and intersecting circles is the most efficient way of being able to construct a triangle with the three-edged lengths.

Before we start any construction, we need to prepare our equipment.

And so you need to have a sharp, ideally a short pencil, a tightened pair of compasses so that they don't stretch and move easily.

You want there to be a little bit of resistance when you're trying to open up the legs of the pair of compasses and a ruler.

The ruler needs to have the scale clear.

So if any of it has started to worn off, then that's not gonna be useful for making an accurate construction.

Then you need to set up the pair of compasses and you set the pair of compasses up when they are closed, in the closed position, and you want the sharp pencil tip to be level with the needle point of the pair of compasses.

So check in on that.

Which of these is the best setup of a pair of compasses? Pause the video whilst you look through those images and decide which set is the best setup.

Press play when you're ready to check.

So A is the best setup because they're closed, the pencil tip is sharp, and it's level with the needle point of the pair of compasses.

B, the pencil and needle tips were not level.

You can see the pencil is overhanging.

And did you notice it on C? It was a blunt pencil.

So a blunt pencil is just gonna make the lines that you draw more thick and therefore you're gonna lose the accuracy of your measurements.

The blunt pencil could potentially be as wide as three millimetres and then your accuracy is dropping.

So a nice sharp pencil so that you've got as thinner point as possible and then set them up whilst they're closed and level.

So we're now gonna look at how to construct a triangle with edge lengths, eight centimetres, five centimetres, and six centimetres.

So this is a scaling triangle because all three edge is of different lengths.

First of all, use your ruler to draw the length of two of the edges somewhere on the page.

They're not part of your construction, but it's a really useful thing to do so that if your pair of compasses do change size during the construction, you can go back and reset them.

It's much easier to set them up on a line than trying to do it against your ruler edge.

So draw two of the edges separately on your sheet of paper, then you'll use them to make sure your pair of compasses are the correct width.

So the five centimetres is being drawn just off to the side and that's gonna allow us to set the pair of compasses to five centimetres really easily.

And the same thing for the six-centimeter edge.

So now we're gonna start the construction by drawing the third edge, the one that you haven't drawn as part of your setup.

And so in this case, for this example, it's an eight centimetre line and you need to do this accurately using your pencil and ruler.

Once you've drawn this base edge of the triangle, label it up.

This is eight centimetres.

So we're now gonna start by locating all of the positions that are five centimetres away from one end of this eight-centimeter line.

Because remember, we're trying to locate the third vertex.

We've got the first and the second vertex of the triangle at either end of the line segment that we've just drawn.

And the third vertex is a fixed distance from both ends and we're using the pair of compasses to locate all of the potential positions and where they've intersect is going to be the location.

So we're gonna use the five centimetre line to set up the pair of compasses.

To put the needle point at one end and stretch it to the other.

Be very accurate with this.

Make sure it is going to five centimetres.

It's not just a little bit short or a little bit over.

Take the time to set them pair of compasses up accurately.

You're now going to move the pair of compasses from your setup line to one end of your eight-centimeter line.

And with this, we're gonna draw a full circle.

We could draw an arc, but then we might miss the intersection.

So we're gonna draw a full circle.

Any point along the circumference of that circle is five centimetres from the end of the eight-centimeter line segment.

So our location of the third vertex is somewhere on that circumference.

We're going to do the same thing, but this time we're setting up to six centimetres and we're going to place the pair of compasses on the other end of the eight centimetre line segment.

So stretch it out to six centimetres, make sure you're being accurate, then place it on the other end, the needle point of your pair of compasses on the other end of the line segment.

Draw the circle here and that shows all the points that are six centimetres from that end of the line segment.

We've located two positions for the third vertex.

We only need to mark one of the points of intersection to be our triangle.

So we mark the intersection, we've marked the one above the line here.

Then you're gonna join that vertex with the ends of the eight centimetre line.

Obviously, using your ruler to make sure that is very neat.

We're not using the ruler there to measure because we've done the circles to do the measuring, but we're using that as a straight edge to just ensure that it is a line rather than a curve.

And we can label our edges.

So we've now accurately constructed a scaling triangle with the lengths eight centimetres, five centimetres, and six centimetres.

So check.

The construction has been done, but where are the three vertices of the triangle? Pause the video whilst you decide where the three vertices of the triangles are.

Then when you're ready to check, press play.

So here are three vertices for a triangle, the ends of the line segment that was drawn using the ruler and the point of intersection between the two circles.

However, you could have used the point of intersection below the line and that still would've constructed a triangle.

It's just a reflection like we saw with Lucas'.

So we're now gonna go through another example of constructing a triangle, but this time it's been written in a slightly different way.

So we're gonna construct triangle PQR.

So we know that they are the vertices of this triangle.

And we are then told that PQ is seven centimetres, PR is nine centimetres, and QR is 10 centimetres.

So it's scaling because all three edges are different.

It's always useful when it's in words and there's no diagram.

And specific edges have to be specific lengths to do a quick sketch.

And this is when we'll just use a freehand sketch or a drawing.

The triangle's got three vertices, P, Q, and R.

I'm just gonna place them around.

It's not about having it accurately sketched, it's about taking the information from the words into a diagram which will allow me then to construct it more easily.

So using the information that was given, PQ is seven centimetres.

We were then told that PR is nine centimetres.

And finally, the line segment between Q and R is 10.

Remember that this drawing is not accurate.

And so the nine centimetres there is actually a longer line segment than the 10 centimetres is not drawn to scale, but it allows us to sort of get an idea of which edges are where.

So we can now start the construction and we're gonna start by drawing the lines of two of the edges elsewhere.

So I can draw a seven centimetre because that is one of the edges of the triangle.

Draw a nine centimetre because that's another edge of the triangle.

And then we will use our pencil and ruler to draw accurately QR, which is the 10 centimetre line.

So I've labelled it up, I know that that is the line segment QR and I know that from the words, but I also know that from my sketch.

So now I'm gonna use the lines that I've drawn to the side to set up my pair of compasses.

So this one is now seven centimetres wide.

When I draw a circle, it will locate all of the positions that are seven centimetres away from Q.

And this is where our sketch is really useful because I need the seven centimetre line to come off from Q, whereas in the last example, it didn't matter which end I put my pair of compasses.

This time we have specifically been told which line segments are which lengths.

So I've drawn my circle to show all of the positions that are seven centimetres away from Q.

And now I'm going to use my line to set up my pair of compasses to nine centimetres and this one needs to start at R.

The needle point of the pair of compasses will go to R.

Now, the sort of working of the construction has been drawn.

We've located two points where P could be.

P could be here, and then you're gonna connect the three vertices to finish the construction.

So we know that P two Q is seven centimetres and P two R is nine centimetres.

However, we could have chose the point of intersection below the QR line.

That could have been the position for P.

So if we connect them up, we have still constructed the triangle PQR is seven, PR is nine, and QR is 10 centimetres.

So Laura wants to practise constructing triangles.

So she's decided she's gonna roll a pair of dice and sum the numbers to get an edge length.

She did it two more times to get three lengths.

So on her first roll of two dice, she got a three and she got a six, which means she's gonna construct a triangle with an edge length of nine centimetres.

She does that two more times to get her three edges because it's a triangle.

So she's got an edge two of 11 centimetres and an edge three of three centimetres.

She has drawn the 11 centimetre edge with her ruler.

She's drawn a circle of radius of nine centimetres from one point and a radius of three from the other.

They're her two other edges.

And where they intersect, she's chosen the intersection above the line she's joined up to create her triangle.

And so she has successfully constructed this triangle with these three edges.

So she repeats the process to get some more practise.

So edge one is five, edge two is six, and edge three is 12.

This time the three edges do not form a triangle.

Why is that? Look at her construction.

She drew the 12 centimetre edge.

She's drawn a circle with a radius of five at one end and a circle of a radius of six at the other end.

But that hasn't constructed a triangle.

Oh, firstly, the two circles do not intersect and the third vertex is always been located when the intersection of the circles.

And the sum of the two radii is not enough.

Five add six is 11.

And therefore, it's not intersecting.

So Laura thinks that the sum of the two shortest edges needs to be at least the longest edge.

So we just saw five plus six is 11 and the longest edge was 12.

So Laura thinks, "Well, it's got to be at least 12." So she tries this with three new edges.

Edge one being five, edge two being seven, and edge three being 12.

And this is the construction that she ends up with.

Drawn the 12 centimetre with her pencil and ruler, constructed a circle of radius five from one end of the 12 centimetre line, and a seven centimetre radius at the other end of the line segment.

How'd she constructed a triangle? So this times the two circles do intersect, but it hasn't formed a triangle.

Why not now? So the two circles are touching rather than overlapping.

The sum of the two radii needs to be more than the longer edge because otherwise they have intersected, they have touched on the baseline, and so it's not created a triangle.

So a check on that.

Which of these would form a triangle? Pause a video whilst you decide which of those would form a triangle.

And then when you're ready to check, press play.

So A would form a triangle, the two shorter edges.

So the three and the five have a sum that is more than the longest edge.

Three add five is greater than seven.

B and C do not form a triangle because it doesn't hold that the two shorter edges are more than the longest edge, but D does because three add four is more than five.

So you're now gonna do some constructing of scaling triangles by yourself.

So for question one and two that are on the screen, question one, you need to construct this triangle accurately.

Remember you're gonna be using a pencil and ruler, but also a pair of compasses.

Question two, you're gonna construct the triangle with edge length six centimetres, eight centimetres, and 10 centimetres.

There isn't a diagram there for you, so you might want to sketch a diagram before you start.

Press pause whilst you're getting on with those questions and when you're ready for the next few questions, press play.

Okay, so question three, four, and five, which are the last three questions of this task are on this screen.

Question three, you need to construct triangle A, B, C given the edge's lengths.

Question four, I would like you to construct the scaling triangle that has an edge of six centimetres, an edge of seven centimetres, and a perimeter of 23 centimetres.

So you need to link back to perimeter with that one.

And question five, similar to question four, but a little bit more freedom.

Construct a scaling triangle with a perimeter of 180 millimetres.

Pause the video whilst you're working on those three questions and then when you press play, we're gonna go through the answers to all five.

So question one, you needed to construct the triangle that was on the screen, but you needed to do it accurately.

So that meant using your pair of compasses, a ruler, and a pencil.

To check your accuracy, measure the marked angles on the diagram with a protractor and they should be 115 degrees and 30 degrees.

Question two, you need to construct a triangle with edge length of six centimetres, eight centimetres, and 10 centimetres.

I drew the 10 centimetre as my base and then used my compasses to draw the six and the eight.

You may have drawn the six and used your pair of compasses to draw the eight and the 10.

Ultimately, we'll have the same construction.

It just might be a rotation or a reflection of the six, eight, and 10 triangle.

So to check that you have done this accurately, measure the angle between the six centimetre edge and the eight centimetre edge and it should be 90 degrees.

So this is actually a right-angled triangle.

Question three, you needed to construct triangle A, B, C.

So I'm hoping that you have labelled your vertices A, B, and C.

You may have done a quick drawing of this first so that you knew which edge was connected to which vertex because that was important.

So you've got 12 centimetres between A and B, five centimetres between A and C, and 13 centimetres between B and C.

So to check the angle between AB and AC should be a right angle, should be 90 degrees.

So use your protractor to check.

Question four was still a construction question, but you needed to do a little bit of work before you could have constructed it.

You were given two of the three edges, you knew their lengths, but you're also told the perimeter.

So because the perimeter is the sum of the edges, and in this case, there needed to be three edges, you needed to work out the third edge needed to be 10 centimetres because 10 plus six plus seven is 23 and you were given the perimeter.

Then you could construct your triangle 'cause you had all three edges.

Once again, to check your accuracy, measure the marked angles with a protractor.

Question five was similar to question four in terms of it was speaking about perimeter, but this time you needed to come up with three edges that would have worked and it may have been that you found an impossible triangle as part of your working.

So the perimeter needed to be 180 millimetres.

And an example of a correct answer here would be 60 millimetres, 50 millimetres, and 70 millimetres.

Remember that 10 millimetres makes a centimetre.

So a perimeter of 180 millimetres is the same as saying a perimeter of 18 centimetres.

So my example here is six centimetres, five centimetres, and seven centimetres.

Okay, so we're gonna move on to the second part of the lesson, which is constructing triangles that which now have equal edges.

So Aisha has been asked to construct an isosceles triangle with edge length of seven centimetres, seven centimetres, and five centimetres.

So it's isosceles, it's got two equal edges.

So what edge should she draw with her ruler? Just pause for a moment and think about that question.

It's actually a right or wrong answer here.

For efficiency, she should draw the base edge, which is the edge that is different to the other two because then she'll only need to set the pair of compasses up once.

So remember when it was a scaling, you needed to change the your pair of compasses during the construction because all three edges were different.

Whereas here we've got two edges that are equal.

So we may as well use the pair compasses to draw both of those and only need to change them once.

Just like the construction for scaling triangle, she's gonna draw that seven centimetres somewhere outside of her construction so that she can set her pair of compasses up very accurately and refer back to it if she needs to if they slide or slip.

So we've got our seven centimetre line.

She's now gonna draw the baseline of her triangle, which is gonna be five centimetres.

Set the pair of compasses up to seven and move it to one end of the line segment that you have drawn.

Draw your circle, remember that locates all the points that are seven centimetres from that end of the line segment, and this is where the efficiency part comes in.

We don't need to change the distance between our pair of compasses because it's still staying at seven.

You could check it against the line to make sure it hasn't changed, but you don't need to reset it up.

All you're going to do is place it at the other end of the line segment and draw us a circle of radius seven centimetres from there.

We've got our intersecting line.

It fits the idea that the two shorter edges, which is five and seven, is greater, is more than the longest edge, which is gonna have to be seven in this case.

So five and seven is 12.

12 is more than seven.

So that's why we do construct a triangle.

Here is the point of intersection, which is a location of our third point because that is seven centimetres from one end of the line segment five and seven centimetres from the other end.

Use our pencil and ruler to accurately draw in them edges and we can label them.

And we can also put the hash marks on there to indicate that they are equal in length because it is an isosceles triangle.

When we construct the triangle with full circles, we find two points of intersection and we only choose one of the points of intersection to construct our triangle.

So we do not actually need to draw full circles, we can just draw arcs instead.

So here is the same construction of Aisha's, but without drawing four circles, only arcs.

That's our line for setting up our pair of compasses.

Draw the base, set up the pair of compasses, place the needle at one end of the line segment, and we've only drawn an arc.

So this is the difference.

We've not drawn a full circle, we're only drawing an arc.

You're gonna have to make sure your arcs are fairly long to ensure you find a point of intersection.

However, if you don't, you can go back onto the point and draw a longer arc.

You've got your lines on the edge of the page to set up your pair of compasses accurately again.

So she's just done exactly the same, but from the other end because there were seven centimetres we didn't need to reset up the pair of compasses.

We've got our point of intersection, and then we've got a full construction of our isosceles triangle.

So to minimise the amount we need to draw, we don't have to draw full circles.

There's nothing wrong with drawing the full circles, but you could for efficiency, only draw arcs.

And if they don't intersect, to just extend the length of the arc.

So quick check.

What is the next step in this construction? Pause the video whilst you decide.

When you're ready to check, press play.

So the next step is to mark the third vertex, which is where the two arcs intersect and then form the triangle using line segments.

Here we've got Jacob and Jun who have both constructed isosceles triangles with edges of six centimetres and nine centimetres.

And here you can see they've only got arcs, they've not got full circles.

So when we're constructing isosceles, you do need to be careful that there could be two answers.

When Aisha was drawing, you were told seven, seven, and five.

So it was explicitly told that the two equal edges were seven centimetres.

Here, they were just constructing isosceles triangles with edges of six and nine.

So Jacob has gone for an isosceles where the nine centimetres are the equal edges, whereas Jun has constructed an isosceles triangle where the six centimetres are the equal edges.

Izzy has been tasked with constructing an isosceles triangle where the equal edges are eight centimetres and she doesn't have any other information.

So she draws one of the eight centimetre edges with her pencil and ruler.

Then she draws an arc for the other eight centimetre edge.

In this case, we don't need to draw a separate line because we can use the eight centimetre line to set up our pair of compasses.

So put our needle point at one end of the line segment and open it 'til the other end.

We now know that the radius of the circle that we draw or the radius of the arc that we draw will be eight centimetres.

So she's drawn a nice large arc here nearly back to the horizontal.

So we've got one edge of eight centimetres and a point along that circumference joined to the end where the needle point is will also be eight centimetres.

So we've got our edges of eight.

and there are actually a lot of possibilities for an isosceles triangle with equal edges of eight centimetres.

If she chooses that point on the arc and connects it all up, that would be an isosceles triangle with equal edges of eight centimetres.

The base edge that she drew using the ruler and then the radius from the arc would also be eight centimetres.

So we've got equal edges.

And then when we connect it with that third line segment, we construct this triangle.

But if we chose a different point along the arc, that would still be a radius of eight centimetres from the end of the line segment.

And so it'd still be an isosceles with equal edges of eight centimetres.

And so you can see there are many possibilities with that limited amount of information, which is that the equal edges need to be eight centimetres actually forms a lot of isosceles triangles.

So if we can construct scaling where all edges are different and isosceles triangles where two of the edges are equal, then we can also construct equilateral triangles.

By definition of an equilateral triangle, it has equal edges.

It is a regular triangle.

Choose to draw a base edge of seven centimetres.

Then all of the edges of my equilateral triangle will also need to be seven centimetres because it needs to be regular.

Once again, I don't need to draw a separate line segment to set up my pair of compasses.

I can use this edge to set up the pair of compasses because it needs to be seven.

So needle point on one of the ends of the line segment, stretch it out so that it's the radius of seven centimetres.

Draw an arc.

And without changing the distance, but we can check it using our base edge, put the needle point at the other end of the line segment and draw an arc.

The point of intersection between those two arcs is our third vertex and we know that it is seven centimetres from one end and seven centimetres from the other.

So we have formed an equilateral triangle.

It didn't need to be seven centimetres, that's just what I've chosen to draw an equilateral triangle off.

But the key thing here is that all edges are equal.

So check, which of the following partial constructions would not complete to make an equilateral triangle? So if you were to complete them, would you have formed an equilateral triangle? Pause the video whilst you're deciding.

When you're ready to check, press play.

So C would not complete to make an equilateral triangle.

If that was an equilateral triangle, those arcs would be meeting the ends of the baseline as you can see in A.

So you're now onto your task with the second part of constructing triangles with equal edges.

Question one, XY is an edge of a triangle.

So that's like the one you draw using your ruler.

Which of the points A to G, when joined to XY, would create? So which of those points is the third vertex to create an isosceles triangle, a right angle triangle, and a right-angled isosceles triangle.

Pause the video whilst you're working through that task.

And when you're ready for the next questions, press play.

Okay, so on this screen, you got three further questions to this task.

So question two, construct an equilateral triangle using the line as one of the edges.

Question three, construct an isosceles triangle where the equal edges are nine units and the base edge is seven units.

Use this scale.

And question four, a tetrahedron is a 3D shape with four equilateral triangular faces.

Construct the net of a tetrahedron.

Pause video whilst you're completing those three questions.

And when you're ready for the answers, press play.

So question one, once you've got your head into this task, hopefully you found it okay.

So part A, an isosceles triangle.

For it to be an isosceles triangle, two edges need to be equal in length.

Vertex B is one, two, three, four, five, six circles out from X.

It is also six circles out from Y.

So that is where they are equal in length.

So the radius from X to B is equal to the radius from Y to B.

And that's the same for F.

Okay, so point F is on the seventh circle out from X and is also on the seventh circle out from Y.

C and D were both points that would make an isosceles triangle because the distance between X and Y, if Y is the centre of the circle, X is on the circumference of the largest circle around Y and C is also on the circumference of the largest circle of around Y.

So the distance X to Y is equal to the distance C to Y, and that's why it's an isosceles.

And that's exactly the same for D.

It's a isosceles triangle with quite a large obtuse angle.

B, a right-angled triangle, well, that would be A and E.

So A is directly above X and E is directly below Y.

So when you connect up A, X, and Y, there's a right angle.

And if you connect X, Y, and E, there is a right angle.

And C, there isn't a right-angled isosceles triangle on this diagram.

That's not to say there isn't one or there couldn't be one, but on this diagram there isn't one.

Question two, you need to construct an equilateral triangle using the line as one of the edges.

And because it's an equilateral triangle, the way to check this with your protractor is measure that all the angles are 60 degrees.

Question three, you need to construct an isosceles triangle where the equal edges are nine units and the base edge is seven units.

And you had to use the scale that was given there.

So that was being your ruler if you like.

So setting your pair of compasses up using that line rather than measuring with your ruler.

To check that you've done that accurately, check the angles with a protractor.

The angle between the two equal edges should be 46 degrees.

Both the base angles should be 67 degrees.

And question four was quite a challenge.

So a tetrahedron is a 3D shape with four equilateral triangular faces.

Construct the net of the tetrahedron.

So remembering that a net is when we unfold a 3D shape, there are two distinct nets of a tetrahedron, so you could keep it on its base and then unfold the three other triangular faces down.

And that would be the left hand net.

Alternatively, you can unfold it and it becomes a parallelogram.

So construction wise, it was four equilateral triangles all connected by their bases.

A construction is an accurate drawing using geometry equipment.

Intersecting circles can be used to construct triangles, but remember in your construction, you don't need to draw a full circle.

You can just draw arcs to locate the intersection.

If we are constructing a scaling triangle, then because all three edges are different, three different radii will be used.

If it's an isosceles, then two different radii because there are equal edges on an isosceles.

And if it's an equilateral triangle, it's some circles with equal radii that will be used to construct that style of triangle.

Well done today.

I look forward to working with you again in the future.