Relating side lengths in similar figures

0:00- [Narrator] We're told the following quadrilaterals are similar. These two right over here. Write a proportion equation that we could use to solve for the length of segment LM. And then what is the length of segment LM? So pause this video and have a go at this before we do this together.

0:18So let's just first think about segment LM. So segment LM is this one right over here. And we already know that these two quadrilaterals are similar. So what is the corresponding side on this quadrilateral to LM? Well, it looks like LM, just the way that it is drawn, it is in this little part that is, I guess you could maybe view it the way it's drawn at least, it looks like it is the shortest side of the quadrilateral.

0:50And then that would be this one right over here. There's other ways that you could think about it. You could think about that, look, this line just comes and hits this longest side, line comes and hits this longest side. So there's other ways to think about it, but that's the corresponding side.

1:04Now let's think about the other corresponding sides. And then we could set up some proportions, and there's multiple ways to do it. So the next longest side is this one, and that would correspond to this one right over here. Then the next longest side is that one.

1:21Corresponds to that side right over there. And then I could even leave this last one unmarked. Now, to a proportion equation that we could use. We could either set up ratios within each quadrilateral or between the two. Let's start, let's first think about within each quadrilateral.

1:40I'm having trouble saying the word. So we could say the ratio of LM to MJ, the length of segment LM to the length of segment MJ. So we could write the length of segment LM. The ratio between that and the length of segment MJ. I could write MJ down, but they tell us it is 32.

1:59So I'll just write 32. That is going to be equal to. We could look at the same corresponding sides on this quadrilateral. That is going to be equal to the ratio between 36.8 because that corresponds to segment LM. It's the shortest side here. Two, I'm trying to get all the colors right, the length of segment CB, which is 73.6.

2:26Once again, it's the corresponding side to this orange side right over here, on this smaller quadrilateral. So this is a completely legitimate proportion equation that we could now use to solve for the length of LM. But there are many other ways that we could have done this.

2:42I'll just do another one just for kicks. I could say that the ratio between LM and DC, so let me write it this way. That's actually easier from a color changing point of view. The ratio between LM and the length of segment DC, or the length of segment LM and the length of segment DC, which is 36.8, is equal to, and I'll do different sides.

3:02I could do it between these two orange sides again. But I could now say, lemme do this one right over here. That's going to be the same as the length of segment LK, the ratio of that to the length of segment AD, because those correspond to each other. So this is another proportion equation we could set up.

3:22And there are many, many more we could do. But let's just solve one of them. In fact, lemme just solve this one right over here. If we multiply both sides by 36.8. By 36.8, that cancels and we would get that the length of segment LM is equal to 60 times 36.8 divided by 138.

3:50I will use a calculator for this. I get 60 times 36.8 divided by 138. Is equal to 16, that's a nice clean number. All right, so the length of segment LM is equal to 16, which looks about right. In fact, I probably could have figured that out if I realized that 36.8 is exactly half of 73.6.

4:19I would not have needed a calculator. I could have then said, well, half of 32 is going to be 16, but we're done either way.