• Written By Rashmi_Arun

# Properties of Trapeziums : Definition and Classification

Properties of Trapeziums: We have all heard about the geometrical shape ‘trapezium’ in our mathematics class, but does anyone know where the term originated from? ‘Trapezium’ originated from the green word ‘trapeza’, which means ‘table’. It might be because of the shape of the table that it resembled the geometrical shape of a trapezium that it was called so. There are distinct properties of trapezium that are very helpful to know to solve problems and understanding the trapezium’s applications in real life.

As we all know, principles from Geometry were used in ancient times for calculating the area by dividing it into different shapes and sizes. Trapezium was one of the geometrical shapes that were used for this purpose. In this article, we will learn more details about the definition and classification of triangles based on their angles and sides. So, let us begin!

## Definition of Trapezium

A trapezium is a closed, quadrilateral (a four-sided geometric shape) with one and only one pair of opposite sides that are parallel to each other. We can also call a trapezium a ‘convex quadrilateral’ because the interior angles of a quadrilateral are less than 180°. A trapezium is also a parallelogram of a special kind because in a normal parallelogram, both the opposite sides are parallel to each other unlike in a trapezium.

### Examples of Trapeziums

Do you love popcorn? Who does not? It is a must if you are watching your favourite movie. If you have observed the popcorn container, you will notice that it is a trapezium. Another example that comes to our mind, that we use in our daily life, is a table lamp. Lunch bags, hand bags, wings of an airplane are some examples of trapezium.

### Classification of Trapeziums

Any geometrical shape is classified into different types based on its properties in order to make the calculations easier. A trapezium is no exception. A trapezium is classified based on its angles and sides. Let us understand them in greater detail.

#### Classification of Trapeziums Based on Their Angles

Trapeziums are classified into 3 types as given below, according to their angles.

1. Acute Trapezium
2. Right Trapezium and
3. Obtuse Trapezium

Acute Trapezium: We already know that an acute angle is the one which is less than 90°. So, in an acute trapezium, the two adjacent angles of the longer base are ‘acute’.

Right Trapezium: In this type, two adjacent angles will be right angles (90°).

Obtuse Trapezium: In this type of trapezium, each of the bases will have one obtuse and one acute angle.

### Classification of Trapeziums Based on Their Sides

Based on the length of its side, a trapezium can be classified into

• Isosceles Trapezium – Two sides that are not parallel to each other are equal in length
• Scalene Trapezium – None of the sides are equal in length

### Properties of Trapezium

It is very important to have a clear and in-depth understanding of properties of geometrical shapes as it helps us solve many problems in real life and advanced mathematics. It also gives us an idea of direction and space.

Let us begin by knowing the properties of trapezium a little more in depth. You have already learnt some of them in this article and there are a few more:

1. Trapeziums can one pair of parallel sides;
2. Sum of the interior angles of a polygon are 360°. This has already been stated at the beginning of the article for why a trapezium is called a convex quadrilateral;
3. Adjacent angles on the same side are supplementary in nature, which means, they add to 180°; and
4. Diagonals of an Isosceles triangle (non-parallel sides are equal in length)  are equal in length.

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