Corresponding angles and distances in scaled figures

0:00- [Instructor] What I wanna do in this video is emphasize what makes a true scaled copy and what does not make a true scaled copy. So just as a review, in a scaled copy, we're gonna have corresponding angles, we're gonna have the same measure, and you're going to have the same corresponding scale factor between corresponding sides.

0:20Now what do I mean by that? Well, let me just make a simple example here. So let's say I have this triangle. I'll make it a right triangle, something like that. And let's say I were to have a scaled copy and I would have a scale factor of 2. Well, I might have something like this.

0:43It would look something like this. Now the reason why I can say that this is a scaled copy is that this angle is gonna have the same measure as that angle. We're assuming that these two are corresponding angles. We would have this angle have the same measure as this angle.

0:58And then last but not least, of course, these both right over here are right angles. They have the same measure. So corresponding angles have the same measure, and then corresponding sides would have the same ratio. So for example, this side right over here, if this one is 5, this one over here is going to be 10.

1:19If this one, if this height right over here is 4, then this height right over here is going to be 8. We have the same ratio. We go from this one to that one, we're multiplying by 2. Now it's very important, we have to be dealing with the corresponding side ratios and corresponding angles.

1:39If only one of those is true, you don't necessarily have a scaled copy. For example, if I were to have this figure, and let's say all the sides are of size side length 1, and let's say I have this figure where all of the side lengths are of side of length 2. So if I look at potentially corresponding sides, it looks like I'm just always multiplying by 2.

2:10But is this a scaled copy? Well, no, when you just even visually look at it, it doesn't look like a scaled copy because the corresponding angle measures are not the same. This angle and this angle do not have the same measure. So these are not scaled copies. And likewise, you could have the same corresponding angles, but not have this corresponding scale on the sides and you still wouldn't have a scaled copy.

2:33So for example, let's say I were to draw this figure right over here and I were to draw this figure right over here. The angles are all the same. These are all right angles here in both of these. So it meets the angle criteria, but it does not meet the criteria that corresponding sides.

2:57The ratios between them are going to have or they're going to have the same ratio. For example, this might be of length 1. Maybe this is length of 1, so this is a square. While over here, let's say this is of length 3, and this is of length 2. So we don't have the same ratio.

3:16That's times 3. And this right over here is times 2. So neither of these on the right are scaled copies 'cause it doesn't meet both the angle criteria and the ratio between corresponding sides criteria.