In this video we’re going to look at similar triangles, so we have shapes that are similar to each other, there’s simply enlargements of each other. If they’re enlargements, they must have some corresponding angles that are going to be equal to each other.
The sides are, of course, going to be related related by some kind of scale. Factor could be, bigger could be smaller, so we’ve got an example here. To start with, we have two triangles they’ve been indicated as being similar.
That means their angles are going to be. The same so if we have a red angle there at a red, those two should be the same. Just like our greens are gonna be the same, and our blues are going to be the same, so for first red is 50.
Our second triangle is going to have an angle of 50. If we’ve got a hundred for green, we have a second hundred and a 30 and a 30, and there you go. We have two triangles are similar. The sides are different lengths, but the angles are the same.
So now we’re going to be asked to actually fill in some missing numbers here, so you can do it a couple of ways. You could say: well the angles inside a triangle add up to 180 and do some subtraction, and that should work.
Just fine. Another way is if you’ve got. Two triangles are similar to each other. Well, their angles are going to be the same. So if this green up here is 10, that means this green down. Here is also going to be 10, and if we have a couple of red angles, if one’s 120 must be in the other ones can be hundred and twenty as well.
So the second type of question – you’re going to come across with similar triangles, is going to be calculating some actual links here. When you have a couple of triangles, you need to find it at least one side.
That’S going to be the same here in a sense of the five and the 15 are going to go together. We’Ve got variables around the rest, so, firstly, why don’t we solve for x? So we’ve got the 515, the 4 and the X, so we’re going to set up a proportion here so first step we’re going to take 5/15, we’ll set that equal to 4 and divide that by X – and I want to point out at this time here that We’Ve got a five and a four in the same triangle and those are both going on the top and rxn or 15 or going on the bottom.
So then we want to go boat and solve this. Here we are going to take the X on the bottom and multiply it by the number up top, so that should give us 5x. We shall set that equal to 15 x 4, that should equal 60 and if we want to get X all by itself, we’re going to divide both sides.
Five, so that should give a 60 /. 5 x is going to equal 12. So let’s go ahead and take that 12 and insert that into our diagram. Last part. Here’S are going to go ahead and solve for y. I think again, I’m going to use that five in that 15 and this time I’m going to use the.
Why and the 18 all set exactly I’ll set this up exactly the same as it did before, except now i’m going to have y over 18. I want to go to cross, multiply this time I’ll. Take this. Why and that 15 top and a bottom gives me 15 y and I’ll set that equal to 5 times 18.
That gives me 90. We want to get while by itself, you’ll divide both sides by 15, and that should give us an answer of 6. You can check my math to confirm those answers are correct. So, in conclusion, if you’ve got some similar shapes here, what you need to do is set up a proportion and do some cross multiplying to solve for those missing variables.
Thank you very much.