# Quadrilateral family tree

Categories: gcse geometry

We previously looked at the different types of quadrilaterals. In this article, we will look at how these different shapes relate to each other, in the form of a family tree.

As we go down the tree, each new shape is a *special type* of its parent (or parents). It inherits its parent's characteristics while also adding new ones of its own.

Here is the family tree:

## Quadrilateral

A quadrilateral is any shape with four sides. It is the most general type of four-sided shape.

## Trapezium

A trapezium is a special type of quadrilateral where one pair of opposite sides are parallel.

## Parallelogram

A parallelogram is a special type of trapezium where both pairs of opposite sides are parallel.

Each pair of opposite sides have the same length.

## Kite

There are two equivalent definitions of a kite.

- A kite is a special type of quadrilateral that has two pairs of equal adjacent sides.
- A kite is a special type of quadrilateral in which one of its diagonals is a line of symmetry.

## Rhombus

A rhombus is a special type of parallelogram and also a special type of kite.

- A parallelogram has two pairs of opposite sides that have equal lengths.
- A kite has two pairs of adjacent sides that have equal lengths.

In a rhombus, all four sides are equal. This allows it to satisfy both conditions at the same time.

## Rectangle

A rectangle is a special type of parallelogram that has four 90-degree angles. Like a parallelogram, the two pairs of opposite sides have equal lengths.

## Square

A square is a special type of rectangle that has all four sides the same length.

It is also a special type of rhombus that has four 90-degree angles.

A square inherits its four 90-degree angles from the rectangle and its four sides of equal length from the rhombus.

All squares are the same shape. This means a square is the most specialised quadrilateral.

## See also

- Regular polygons
- Interior and exterior angles of a polygon
- Triangles
- Quadrilaterals
- Pentagons - polygons with 5 sides
- Hexagons - polygons with 6 sides
- Heptagons - polygons with 7 sides
- Octagons - polygons with 8 sides
- Nonagons - polygons with 9 sides
- Decagons - polygons with 10 sides
- Hendecagons - polygons with 11 sides
- Dodecagons - polygons with 12 sides
- n-gons - polygons with any number of sides
- Other types of polygon
- Star polygons

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