How Many Parallelograms Are in a Triangle?

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A certain number of parallelograms can be used to make up a standard triangle. Find out how many parallelograms are in a triangle with help from an experienced math tutor in this free video clip.

Part of the Video Series: High School Math
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Video Transcript

Hi there. This is Ryan Malloy here at The Worldwide Center of Mathematics. In this video, we are going to discuss how many parallelograms are there in a triangle. Well there are two different answers to this question depending on how you define the world in strangely enough. One possible definition of can you put a parallelogram in a triangle means taking the sides and vertices of a triangle, can you connect one vertex to another in such a way that you create a parallelogram and the answer is no here, so in that sense there are zero parallelograms in a triangle. A much more reasonable question to ask would be if you are given a parallelogram how many different triangles can you make out of that? For example you can cross this diagonal here and you get those two triangles, cross the opposite diagonal here, you get these triangles, three and four but then you also get these smaller triangles in here, we'll call five, six, seven, eight. So you could say that you can fit eight different triangles into a parallelogram, but that's not what we're asked. We're asked for how many parallelograms can fit in a triangle. Using this definition there's zero. Of course there's the other definition that you might use. You simply take any parallelogram smaller than a triangle and see if you can cram it inside. So let's just go ahead and draw a parallelogram. Well there's one that can fit easy enough. We'll just make one a little bit larger, there's another one. So using this definition you can essentially fit infinitely many distinct parallelograms into a triangle. So depending on what exactly the question means the answer is either zero or infinity. My name is Ryan Malloy, and we've just discussed how many parallelograms are in a triangle.


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