Identifying similar triangles
About this video
Sal picks out the similar triangles in two sets, each triangle showing two angle measures. Triangles are similar when all their angles match; if two angles match the third must too, because angles in a triangle add to 180 degrees. When no pair matches at first glance, he calculates the missing third angle.
You'll be able to
- decide whether two triangles are similar by comparing their angles.
- find the third angle of a triangle using the 180-degree angle sum.
- explain why two matching angles are enough for triangle similarity.
Key words
- similar triangles
- Triangles with the same shape, meaning all their corresponding angles are equal.
- angle sum of a triangle
- The three angles inside any triangle add up to 180 degrees.
Transcript
- [Instructor] We are told the image shows a set of triangles and two of their angle measures. Select the two similar triangles. So pause the video and have a go at this before we do it together. Okay. So we know that two triangles are similar if all of their angles have the same measure.
Now, in all of these scenarios, they've given us only two angles. And we could use the two angles to figure out the third angle. Or if there's a situation where we already have two angles that are the same, we know that the third angle has to be the same measure as well.
And in this scenario, it looks like A has a 61 degree measure angle, 62 degrees, and so does L, 61 and 62 degrees. So I would immediately say that these two are similar. That is the similar pair there. And if you really wanted to validate it, you could solve for the last angle, the third angle there, but it has to be the same because all the three angles need to add up to 180.
So this is going to be 180 minus 61 minus 62, which is what, going to be 57 degrees in either situation. But we didn't have to calculate that because we already knew that these two were the same. If you didn't already have these two the same, then it would be good to calculate the third just to make sure you aren't missing something.
Let's do another example here. So same type of question. And again, pause this video and see if you can have a go at it. All right, so this is actually the scenario that I just talked about. None of these, at least when I'm eyeballing them, have the exact same two.
So for these, I'm actually going to calculate the third angle here. So this third angle in this situation is going to be 180 minus 103 minus 43 in degrees. So that's going to be what? 180 minus 146. 80 minus 46 is 34 degrees. So this right over here is 34 degrees.
Now, I do already see triangle I has a 43 degree angle and a 34 degree angle. So this one I'm feeling good about. 34 degrees, 43 degrees, 34 degrees, 43 degrees. 34 degrees, and 43 degrees. And so we already know that these two are similar and if you really wanted to validate, you could solve for this last angle, which will come out to be 103 degrees because it's just going to be 180 degrees minus these two.
So these are the similar ones.
Video © Khan Academy, used under CC BY-NC-SA. Watch on Khan Academy. Puzzicle is not affiliated with Khan Academy.