Types of Quadrilaterals Explained (Trapezoids, Parallelograms, Squares & More!)

Welcome to Math with Mr. J. In this video, I'm going to cover some different types of quadrilaterals and how we classify them. We're going to use the hierarchy you see on your screen to organize the quadrilaterals and show how they are all related and also how they are different. Think of it like a quadrilateral chart here to help us stay organized. We're going to start up top and work our way down. As we work our way down, the quadrilaterals are going to get more and more specific, or you can think of it as more and more special. You'll see what I mean as we work through. Now keep in mind, we will be using different properties of quadrilaterals to help us classify parallel sides, right angles, and equal sides. Let's start up top with quadrilateral. A quadrilateral is just any four-sided polygon, like our example there. And remember, polygons are shapes that are flat, closed, and made of straight sides. So this isn't very specific or special here. Any four-sided polygon we can call a quadrilateral. Now let's work our way down to trapezoid. Trapezoids are quadrilaterals, but we are getting a little more specific here. Trapezoids are quadrilaterals with at least one pair of parallel sides. Notice in the example, the left and right sides are parallel. So we have one pair of parallel sides. So yes, this is a quadrilateral. But a better name is trapezoid, because that tells us more information about the shape. Trapezoid tells us that we have at least one pair of parallel sides. Now let's move down to parallelogram. Parallelograms are quadrilaterals, and parallelograms are trapezoids. But more specifically, parallelograms have two pairs of parallel sides. Notice in the example, the left and right sides are parallel, and then the top and bottom sides are parallel. So two pairs of parallel sides. Opposite sides are parallel, so sides across from each other. Now is that example a quadrilateral? Yes, it is a four-sided polygon. Is it a trapezoid? Yes, it does have at least one pair of parallel sides. But more specifically, it actually has two pairs of parallel sides. So the best name is parallelogram. Now as we move down, we have two choices. Go left to rectangle, or go right to rhombus. Both break off of parallelogram, because they are both basically more specific or special parallelograms. Let's break off to the left first, and go down to rectangle. We're going to think of rectangles as parallelograms, so they have two pairs of parallel sides. Opposite sides are parallel. But more specifically, rectangles have four right angles. The name rectangle tells us that we have two pairs of parallel sides, plus four right angles. Now let's go to the right from parallelogram, and go to rhombus. So rhombuses are parallelograms. They have two pairs of parallel sides. But more specifically, rhombuses have sides that are all the same length. So four equal sides. The name rhombus tells us that we have two pairs of parallel sides, and all four sides are the same length. And then lastly, let's move down to our last quadrilateral here. We basically combine all of these properties from above for the most specific and special quadrilateral. And that's a square. Squares are four-sided polygons with two pairs of parallel sides, four right angles, and all four sides are the same length. So for that square there, can we call it a quadrilateral? Yes, it is a four-sided polygon. Can we call it a trapezoid? Yes, it does have at least one pair of parallel sides. Can we call it a parallelogram? Yes, it has two pairs of parallel sides. How about, can we call it a rectangle? Yes, it does have those four right angles. How about a rhombus? Yes, all of the sides are the same length. But the best name is square. Square tells us that the shape has all of those properties. So basically, to recap here, any four-sided polygon is a quadrilateral. If a quadrilateral has one pair of parallel sides, the best name is trapezoid. If a quadrilateral has two pairs of parallel sides, the best name is parallelogram. If a quadrilateral has two pairs of parallel sides and four right angles, the best name is rectangle. If a quadrilateral has two pairs of parallel sides and all four sides are the same length, the best name is rhombus. And then lastly, if a quadrilateral has two pairs of parallel sides, four right angles, and all four sides are the same length, the best name is square. Now that we know a little bit more about those types of quadrilaterals, let's take a look at more examples and see if we can classify them. So we have four quadrilaterals here and we need to give them the best and most specific name possible based on their properties. Now for each of these, could we say they are all just quadrilaterals and put that for all four? Yes, technically that is correct. They all are quadrilaterals, but that's not the best name for these. There are better names that give us more information about the shape. Let's jump into number one. Now my suggestion, start at the top of the hierarchy or the chart and work our way down to find the best name. So for number one, is this a quadrilateral? Yes, but let's go down to trapezoid. It does look like we have one pair of parallel sides here, the top and bottom sides. So with one pair of parallel sides, we do have a trapezoid. Now can we go down to parallelogram? Do we have two pairs of parallel sides? No. So the best name for this quadrilateral is trapezoid. One pair of parallel sides. Moving on to number two, it looks like we have a quadrilateral with two pairs of parallel sides. So this is a parallelogram, but more specifically, we have those four right angles as well. So our best name here is rectangle. Moving on to number three, we have a quadrilateral with two pairs of parallel sides. So yes, this is a quadrilateral. This is a trapezoid, at least one pair of parallel sides. But since we have two pairs of parallel sides, the best name is parallelogram. Lastly, for number four, we have a quadrilateral with two pairs of parallel sides, and all four sides are the same length. So this is a quadrilateral, this is a trapezoid, and this is a parallelogram. But since all four sides are the same length as well, the best name is rhombus. So there you have it. There's an overview of some different types of quadrilaterals and how we classify them. I hope that helped. Thanks so much for watching. Until next time, peace.