Types of TRAPEZOIDS and their characteristics

In this new lesson that we bring you from a Teacher, we want to make it easier for you to understand and study the polygons that exist in plane geometry, specifically of the trapezoids. In this way, we will see what a trapezoid is, what types there are and what their characteristics are. At the end of the article you will also find an activity to reinforce what has been explained and its respective solution. If you want to know the different types of trapezoids and characteristics, keep reading!

A trapezoidit's a four-sided irregular polygon, that is, a quadrilateral, which are not parallel to each other. For this reason they are considered non-parallelograms. In this way, as in a square or a rectangle the sides are parallel two by two, in the trapezoids they are not, so it is the trick that we are going to use to differentiate them. Up to 3 sides can be equal in length. In addition, this flat geometric figure always has two diagonals, which can be interior or exterior, as we will see below.

It is important to mention that do not confuse a trapezoid with a trapezoid, since the second has two parallel sides, while the first, as we have already said, does not have any parallel sides.

Properties of trapezoids

We are now going to comment on some properties that are remarkable. We can inscribe a trapezoid in a circle if the Sum of two opposite angles gives 180 °. We can circumscribe a trapezoid in a circle if the sum of one side and its opposite is the same as the sum of the other side with its opposite.

What's more, none of the four sides trapezoid its base is considered, except if it is specified that one of the sides is. They can even have three acute angles, although in the case of crossed trapezoids, as we will see in the next section, they can have up to four acute angles.

We will classify the trapezoids according to two criteria: concave / convex, symmetric / asymmetric. So, we are going to see its most characteristic aspects.

• Concaves: they have an inside diagonal and an outside diagonal. That is, if we join their opposite vertices, the resulting lines remain one inside the trapezoid, but the other outside.
• Convex: both diagonals are interior. On this occasion, if we join the opposite vertices, the resulting lines pass through the interior of the trapezoid.
• Asymmetrical: they have different sides, so we can consider them scalenes. It should also be noted that there are crossed trapezoids, which are asymmetric trapezoids in which two of their sides intersect. These have their two outer diagonals. They might resemble an hourglass with no side parallel to the other.
• Symmetrical: they have an axis of symmetry and their consecutive sides are equal to each other two by two. This means that if we split the figure, we will have the same but the opposite. If they are convex, they are known as a spearhead, while if they are concave they are known as an arrowhead, due to their similarities. In addition, depending on the opening of the angle, it can be considered acute, rectangle or obtuse. To remember the types of angles you can enter this article. In general, symmetrical trapezoids are often called deltoids or kites. Its diagonals are perpendicular.

As you have seen, these categories are mixed with each other. That is, a trapezoid can be concave and symmetrical, for example, but it cannot be concave and convex at the same time, nor symmetric and asymmetric at the same time.

To check that you have correctly understood what a trapezoid is, what types there are and what their characteristics are, we propose the following exercises, of which you will find the solution below.

1. Tell what type of trapezoid has only one outer diagonal and one axis of symmetry.
2. Find a trapezoid in the following image:

We are gonna give response to proposed activities, so you can check if you have understood everything that we have explained in today's article about trapezoids:

1. It is a symmetrical concave trapezoid.
2. You may have found others, but the largest and most visual is the one between the second windmill that is seen in its entirety and one from behind.

If you found this article interesting, do not hesitate to browse the top search engine on the web or the tabs of the Mathematics subject. Specifically, we recommend that you continue studying the polygons that exist, to have a broad knowledge of Geometry.