Video: Identifying Similar Triangles

Which two of these triangles are similar?

02:33

Video Transcript

Which two of these triangles are similar?

In order for shapes to be similar, they must have corresponding sides that are proportional and corresponding angles that are equal. So for sides to be proportional, that means maybe one is smaller than the other. So say one that’s smaller has the side length of one and then the other corresponding side on a larger triangle has a side length of three. That means its side of the larger triangle is three times larger than the smaller triangle.

So if the smaller triangle had another side length of two, that corresponding side of the larger triangle must be two times three. It must be three times bigger. So it must be six. And the corresponding angles must be equal. So they must be exactly the same.

So let’s look at the sides being proportional. These two triangles have two side lengths that are congruent. So they would be considered isosceles. And these two triangles are both equilateral because all of their sides are equal. So one and three have corresponding side lengths that are proportional.

Let’s say that the smaller triangle — number three — has side length of one, then the larger triangle — triangle number one — say it has a side length of three, then they all will be three. So each of those sides would be three times larger than the smaller one, just like we said in our example. And the same could be true for two and four. Say these are lengths of four and these are lengths of eight. Those sides will be twice as large. They will be proportional.

Would this make the last two sides proportional? Well, before we give that too much thought, what about the fact that the corresponding angles must be equal. How are we going to know what these angles are equal to? We won’t.

However, with equilateral triangles, all of their angles are equal. And actually a triangle has a total of 180 degrees. So if we split that equally between three angles, we get 60 degrees. Therefore, we would know that for triangles one and three, their corresponding angles will be equal. And we already know that the corresponding sides are proportional. Therefore, triangles one and three will be similar.

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