What is a Rhombus? | Quadrilaterals | Math with Mr. J

[Music] Welcome to Math with Mr. J. In this video, I'm going to cover what a rhombus is. Now, simply put, a rhombus is a quadrilateral with all four sides equal in length. Let's take a look at some examples and dive in a little further. So, rhombuses are quadrilaterals. They have four sides. Now, more specifically, rhombuses are parallelograms. They have two pairs of parallel sides. Opposite sides are parallel and the same length. Opposite angles are the same measure as well. And to take that a step further than just a parallelogram, a rhombus has to have all four sides equal in length. So all of the sides are the same. So looking at example A right here we can see that we have a quadrilateral. This is also a parallelogram. Opposite sides are parallel and we can mark that using arrow symbols. So one arrow here and here show that those sides are parallel and then two arrows here and here show that those sides are parallel. Opposite angles are equal in measure as well. So we can show that with arcs. We will use one arc for this pair of opposite angles and then we'll use two arcs for this pair of opposite angles. So the opposite angles with one arc have the same measure and then the opposite angles with two arcs have the same measure. And then all four sides are equal in length. So we can use a tick mark on each side to show that all four sides are the same length. So a tick mark here, here, here, and here. That's an example of a rhombus. Just remember rhombuses are quadrilaterals with all four sides equal in length. Let's move on to example B. Now here it looks like we have a square. So is this not a rhombus then? Well, we have a quadrilateral with all four sides equal in length. Let's put a tick mark on each side to show that each side is the same length. And this is a parallelogram as well. We have two pairs of parallel sides. We're not going to label those like we did for example a though. So yes, this is actually technically a rhombus. When we hear rhombus, that tells us we have a quadrilateral with all four sides equal in length. And that's what we have here. So yes, a square is a rhombus. A square is a quadrilateral with all four sides equal in length. Now, please keep in mind rhombus is not the best name here, though. It's not the most specific or fitting square is. We call this a square because that gives us more information about the shape than just rhombus. So square tells us that not only do we have features of a quadrilateral, parallelogram, and a rhombus, but we also have four right angles. And we can mark those right angles with squares. So that tells us we have 90° angles. So basically a square is a more specific or special rhombus. Let's move on to numbers 1 through 4 where we will determine if we have a rhombus or not. Green check means yes. Red X means no. Looking at number one, we have a quadrilateral with all four sides equal in length. So yes, this is a rhombus. We have all right angles here as well. So although this is a rhombus, the best and most specific name here is square. Moving on to number two, we have a quadrilateral and all four of the sides are the same length. So yes, this is a rhombus as well. Moving on to number three, we have a quadrilateral, but all four sides are not the same length. These sides are equal in length with one tick mark. And then these sides are equal in length with two tick marks. So no, we do not have four sides that are the same length. This is not a rhombus. And then lastly for number four, we have a quadrilateral, but all four sides are not the same length. So this is not a rhombus. So there you have it. There's a basic overview of what a rhombus is. Just remember a rhombus is a quadrilateral with all four sides equal in length. I hope that helped. Thanks so much for watching. Until next time, peace.