 This video is called Similarity Statements and Scale Factor 2. It is very similar to the video that you just watched, except the instructions have a few more things we have to complete and the picture looks a little bit different. This one says to write a similarity statement, find x, find the measures of segments gp and fg, and find the scale factor. Alright, so there's a lot of things we have to do when we're all done. We'll make sure we've covered them all and we'll just take it one step at a time until we complete it. When you look at this picture, it's a little bit different than the last video. In the last video, we had two similar triangles that were sitting right next to each other. In this picture, it looks like the small triangle is almost sitting in that corner embedded inside the bigger one, or sitting on top of it you could almost think of. So you can see that the smaller guy is here and the bigger triangle is the whole thing. What I think I'm going to do is I'm going to leave the small triangle as it is, but I'm going to draw the big one over again. So when I do that, I get sides of f, g, and h. And now I'm going to redo their side lengths. Let's look at the left side of gf. It looks like we've got a 2x plus 8 and a 12. Well, I can combine that to become 2x plus 20. So the entire side of my big triangle is 2x plus 20. The entire side of my small triangle is 2x plus 8. Let's do the same on the right hand side. gh looks like it's 8 plus 16. Since those are like terms, I can combine them to 24. So the right hand side of my large triangle is 24. The right hand side of my small triangle is 8. All right, so let's start with a similarity statement. Remember, similarity statement is simply naming what the similar triangles are and pairing up the vertices together in the correct way. So I can name my first triangle anything I want. I'm going to name my small one pgq. Okay, the smart board does not want to work over there. Let me try again, triangle pgq. I'm sorry, that's hard to read. Hopefully you can see that. And that will be congruent. So now we have to name, or I'm not, I'm sorry, not congruent similar to our big triangle. Well, if we did pgq, it looks like we went from the left to the right. So we'll have to do the same thing and do fgh. All right, again, not the neatest writing the smart board is being a little bit difficult. Hopefully you can read that. All right, so this would be our similarity statement. So the first part of our problem is done. Now to work on finding x in the scale factor, we have to pair things up correctly. So let's go back to our picture. And remember, the 2x plus 8 matched with the 2x plus 20. And it looks like the 8 matches with the 24. So the left-hand side of the small triangle matches with the left-hand side of the big triangle. And the right-hand side of the small triangle matches with the right-hand side of the big one. This will allow us to set up a proportion and solve for x. Excuse me, so let's look. We said that the 2x plus 8 matched with the 2x plus 20. And we also said that the 8 matched with the 24. So what I did is I just created a proportion where I'm going to have to cross-multiply. And before I do that, I noticed the 8 over 24. Let's make those numbers a little smaller. This could reduce down 8 goes into 8 once, 8 goes into 24 three times. This simply just makes our math a little bit easier. If you didn't notice to reduce it and you used 8 over 24, you would still get the right answer. So when we cross-multiply, we're going to do 3 times 2x plus 8. And we're going to do 1 times 2x plus 20. All right, well, we have to distribute on the left. 3 times 2x is 6x. 3 times 8 is a plus 24. And on the right, when you distribute 1 times 2x plus 20, you just get 2x plus 20. So let's keep going. We're going to subtract 2x from both sides. And we're going to subtract 24 from both sides. So we get 4x, those cancel, equals those cancel minus 4. So when you divide both sides by 4, you get x equals negative 1. So we just found our second answer. All right, so we have two parts of our problem done. And I have run out of room on my screen. So I'm just going to go to the next screen. I kind of have recapped here what we've done. I wrote the similarity statement here. And that x equals 1 here. If you still need more time to copy down the work for how we got to x equals negative 1, just rewind the video and pause it and watch it until you have everything written down. As you can see, I redrew my two triangles where we had them split up, the smaller one and the larger one with their side lengths. All right, so we've done similarity statement. Find x. Now we're going to find the measure of gp. Well, gp is on the smaller triangle. It looks like it was represented by a 2x plus 8. And we found x to be negative 1. So I'm going to replace the x with a negative 1. And let's see, what do we get? 2 times negative 1 is negative 2. Negative 2 plus 8 is 6. So it looks like gp is 6 units long. All right, and then they want us to find the length of fg. Well, fg is represented by 2x plus 20. So when I replace the x with a negative 1 here, you end up with a negative 2 plus 20, which will be an 18. So it looks like fg can be replaced with an 18. So there I took care of finding the lengths of gp and fg. Now the only thing left I have to do is find the scale factor. The reality is you've already found it and used it once, but let's just review to make sure you remember what it is. The scale factor tells you how much your triangle is changing by. And it's important to remember that for triangles to be similar, all the side lengths have to change by the same amount. So we have to compare their lengths. Remember, the 6 is going to match with the 18 and the 8 is going to match with the 24. So if you make fractions, 6 goes with the 18 and 8 matches with the 24. Well, both of these, 6 and 18 can be divided by 3. I'm sorry, it can be divided by 6. So you end up with 1 over 3. Now hopefully my other fraction will be the same thing. And sure enough, it works. 8 over 24, you can divide top and bottom by 8. So you end up with 1 over 3. So your scale factor is 1 third or it's 3. I would, this is Mrs. Milton. Mrs. Milton would accept 1 third or 3 as a scale factor. Talk to your teacher about which one if they would accept both or if you'd have to do one or the other. To me, it just depends how you set up your fractions. Did you do 6 over 18 and 8 over 24? Or did you do 18 over 6 and 24 over 8? Personally, it doesn't matter to me as long as you stay consistent with how you do the first one, you have to do the second. So I think we've taken care of everything. We've written a similarity statement. We found X, we found the lengths of GP and FG and we found our scale factor. Good luck doing problems like these on your own. Remember, consult your notes. Hopefully you took now good notes, neat notes that you could refer back to and understand what you did. If you have any questions, see your teacher tomorrow. Thank you.