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# Similarity Examples | Similarity Example Problems | Similarity | Geometry | Khan Academy

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## Similarity Example Problems | Similarity | Geometry | Khan Academy

Transcript:

In the first task we want to find segment length, segment CE. We have these two parallel lines. AB is parallel to DE. We have these two intersecting, of these two triangles. Let’s see what we can do. The first thing that may come to mind is that this angle and this angle are opposite (vertex) angles. So, they will be equal. Another thing you can think of is that the angle CDE is named after the angle CBA. We have this intersection here and these will be cross angles – that is, they will be equal. If we continue this intersection, we will get the corresponding angle with CDE here. And this one is just the opposite. Either way, this angle and this angle will be equal. So, we found that we have two triangles. And they have two corresponding angles that are equal. That, in itself, suffice it to say that triangles are similar. In fact – In fact, we can say that this and that angle are also equal as cross angles. But it is not necessary. We already know that they are similar. In fact, we can say that at the cross angles, they will also be equal. But we already know enough to say they’re similar, even before we do that. We have already met this triangle. I will try to color it so we have it identical corresponding vertices. It is very important to know which angles correspond to which countries so as not to confuse the proportions, and to know what corresponds to each other. Thus, we know that triangle ABC is similar to triangle .. And this peak A corresponds to peak E right here – is similar to peak E. A peak B here corresponds to vertex D, EDC. How does this help us? This tells us the proportions of the respective countries will be equal. They will be equal. They will be a constant. So, we have a corresponding country .. The proportion, for example, the corresponding side of the BC will be DC. We can see it. Just about the way we proved the similarity. If this is true, then BC is corresponding to the DC side We know that BC, the length of BC on DC, right here, will be equal to the length of .. First we have to find how much CE is, this is what interests us. I use BC and DC because I know their values. Thus, BC over DC will be equal to of the respective CE country. The relevant country here will be CA .. It will be equal to CA on CE corresponding countries. This is the last and the first, the last and the first ARE on CE. We know how many aircraft, The aircraft here is 5. We know how much DC is She is 3. We know how many CAs or ACs are here, CA is 4 And now we can calculate the CE. We can there are many ways you can calculate it. Multiply by the cross, which is actually a multiplication of the numerator by the denominator. We get 5 along the length of the CE, which is equal to 3 by 4, which in turn is equal to 12. that’s how we get CE. CE is equal to 12 over 5. This is the same as 2 and 2 fifths. or 2.4 This will be 2 and 2 fifths We’re ready. We used the similarity to get this country, as we simply knew that the proportions between the respective countries will be the same. Let’s solve this problem here now. Let’s look at this one here. I will draw a small line here. This is a different task. Here we want to find how much is DE. Again we have these two parallel lines. We know that the corresponding angles are equal. We know that this angle will be equal to this angle. Because this can be considered intersecting here. Also, we know this angle here will be equal to this angle here. Once again, we have corresponding angles for the intersections. In both triangles. I’m looking at CBD and CAE triangles. They share a common corner here. In fact, we showed once again that we can stop at two angles. We really showed that all three angles of these two triangles, all three corresponding angles, are equal to each other. Now we know .. The important thing we need to do is once again to make sure we get what you write, in the right order, when we prove the similarity. Now, we know that triangle CBD is similar, not equal, is similar to triangle CAE. This means that the relationship between the parties concerned will be a constant. We know, for example, that the relationship between CDs it will be the same such as the relationship between CB to CA. Let’s write it. We know that CB on CA will be equal to the ratio between CD on CE. We know that CB is, CB here is 5. We know how much is CA? We have to be very careful now. Not 3. SA, this whole country will be 5 plus 3 This is equal to 8. We also know that CD is, CD will be 4. Now we can multiply crosswise again. We have 5 CE, 5 CE equals 8 to 4 8 by 4 is 32. So CE is equal to 32 over 5. Or we can present it in another way. 6 and 2 fifths. We are not ready because we are not looking for how much CE is. Only this part is wanted here. Search with is DE. We know the whole length, CE here. She is 6th and 2nd fifth. So, DE is here what we need to find. It will be equal to this length, 6 and 2 fifth minus, minus CD. This will be equal to 2 and 2 fifths. 6 and 2 fifths minus 4 is 2 and 2 fifths. We’re ready! DE is 2 and 2 fifths.

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