Determining similarity in polygons

0:00- [Narrator] All right. What we have here is three pairs of quadrilaterals. And the goal here is to figure out if each pair is actually dealing with similar quadrilaterals. So pause this video and have a go at that. All right. So to establish similarity in quadrilaterals, you actually have to be a little bit stricter than you are with triangles.

0:24You have to have both conditions met. That all of the corresponding angles have the same measure and the ratio between corresponding sides is the same. So for example, let's look at this first pair here. We see nothing but 90 degree angles in both of them. So they definitely have all congruent angles, or we could say the measures of all of their angles are the same.

0:47So they definitely meet that condition. But let's look at the sides. So if we look at the shorter sides, AD looks like it corresponds to EH. And to go from AD to EH, we multiply by two. And the same thing is going from BC to FG. We're multiplying by two, so that looks good.

1:07But in order for these to be similar, I would have to multiply by two to go from AB to EF. But if I multiplied by two, I don't get to 10. I would get to 12. So these two are not similar. So now let's look at this second scenario here. Well, this is the reverse scenario.

1:28All the sides have the exact same measure. So we meet that condition, but the angles don't have the same measure. In fact, none of the angles have the same measure the way it looks. These are all 90 degree angles. And if these were 90, they would have shown this little right angle symbol here.

1:44So these are not 90 degree angles. So we have none of the corresponding angles are having the same measure. So this is also not similar. So not similar in both of these. Now, this is our last hope right over here. So first let's look at the angles. So this angle corresponds to that one.

2:0490, 90. Both right. This one corresponds to that one. Also 90, 90. 117 degrees, 117 degrees. 63 degrees, 63 degrees. So far, so good. But now let's look at the ratio between the sides. Okay. So we could do this two different ways. Well, let me just do it by looking at the, and we have to be very careful to look at the right corresponding sides.

2:28So if we look at the long side, the longest side looks like it is this side right over there, which would correspond to this side right over there. To go from eight to 16, we are multiplying by two. All right, let's keep going. Let's look at the shortest side.

2:45This TU looks like it corresponds to this XY. To go from four to eight, we are also multiplying by two. So far, so good. Let's go to the next side right over here. That side and that side correspond to each other. And so if we're going from ST to WX, we are going from six to 12, which is multiplying by two.

3:15And then last but not least, we have this side right over here that corresponds to that side. And once again, to go from 4.5 to nine, my hand got squiggly there. We're multiplying by two again. So this one is, this pair is similar. Is similar. So we got one of them to actually work.