How to Use Proportions When Checking Similarity

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Checking similarity sometimes requires you to use proportions when completing a problem. Use proportions when checking similarity with help from a longtime mathematics educator in this free video clip.

Part of the Video Series: Number Theory Education
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Video Transcript

Hi, I'm Jimmy Chang, and we're here to talk about how to use proportions when checking similarity. Now, when it comes to checking similarity, you want to assume, of course, that the shapes themselves are already similar, because you don't want to assume something that's not. So, if you're given that they're similar, then you can use proportions to check that property. So, it often involves uses of shapes, whether it be triangles, rectangles, et cetera. So, let's just look at an illustration, ok. So, suppose you're given that these are similar triangles? And, suppose you're given that this is five, and that's going to be X, and this is going to be, let's just say ten, and that'll be twenty. Now, what you want to think about here is if you want to solve for X, you have to make a decision on if you want to compare, put the smaller numbers on top in the proportion, or if you want the larger numbers on top. Now, whatever path you go, you're going to get the same answer for X. So, let's just, for consistency purposes, put the smaller numbers in the numerator. So, you got to do it in both sides of the equations. So, what you have here is five over--and for the denominator you want to put the corresponding side on the other triangle. So, it 'd be five over ten. That's going to equal to X over the other corresponding side is going to be twenty. And what you want to think about then is, to solve it you want to use cross multiplication. So, the denominator multiplied by the numerator. So, this would be ten X equal to, and then twenty times five is going to be a hundred. And then you want to solve for X, and that's dividing both sides by ten. And the tens will cancel. So, X is equal to ten. So, the missing side would have been ten. And, if there were units involved, you would put the units in the appropriate spots. But, had the equation been modified to where the larger numbers would be on top, you would still get the same number. So, when it comes to using the proportions to checking similarity, you want to be given that the shapes are similar to begin with. So, I'm Jimmy Chang, and that's how to use proportions to check similarity.


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