# Types of trapezoid

The types of trapezoids are the different categories in which those quadrilaterals (four-sided polygons) that have two parallel sides and two other sides that can intersect in their extensions can be classified.

Trapezoid types, therefore, are the different ways in which a four-sided polygon can be presented or classified. Trapezoids can be classified in many different ways. Mainly, by whether the length of its non-parallel sides coincides and by the measure of its interior angles.

We must remember that, as in any quadrilateral, the sum of the interior angles of a trapezoid must be 360º (degrees).

Another point to keep in mind is that a trapezoid is not a regular polygon. This is because it is not equiangular, that is, with all its interior angles equal, nor equilateral, with all its sides the same length.

## Trapezium isosceles

The isosceles trapezoid is one in which its non-parallel sides have the same length. Thus, the following is true:

- In the figure below, the trapezoid is isosceles if AB equals DC.
- The two interior angles that are on the same base (the bases are the parallel sides of the figure) have the same measure. If we are guided by the image below, we would have the following: α = β and δ = γ.
- The diagonals have the same length (AC = DB)
- Interior angles that are on opposite sides are supplementary. In the lower image it would be true that: α + γ = α + δ = β + δ = β + γ = 180º.
- It has two acute interior angles (less than 90º) and two other obtuse angles (greater than 90º). Thus, in the example figure, α and β are obtuse, while δ and γ are acute.
- It has an axis of symmetry that is perpendicular to the bases and cuts them at their midpoint. In this way, when drawing said axis –which is the line EF in the figure below–, the polygon is divided into two symmetrical parts. That is, each point on one side corresponds to a point on the other side, both being equidistant from the axis of symmetry. For example, the distance between point A and point E is the same as that between point E and point D.

## Rectangle trapezoid

The right trapezoid has two right or equal interior angles of 90º. The following is true:

- One of its non-parallel sides is perpendicular to both bases of the trapezoid. That is, at their union they form right angles.
- Their right angles are not opposite, but are adjacent.
- It has an obtuse angle and an acute angle. These would be β and δ in the figure below, respectively.
- The height of the figure is the perpendicular side.
- Their diagonals do not measure the same.

## Scalene trapezoid

The scalene trapezoid is a type of trapezoid whose four sides are of different lengths. Similarly, all its interior angles measure differently, and its diagonals are also unequal.

This type of trapezoid can take different forms, as we can see in the images shown below:

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