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What makes a Quadrilateral?

The short answer to “what is a quadrilateral?” is that it is a four-sided polygon. In other words it is four-sided, two-dimensional enclosed shape with straight sides.

Your children will learn (typically in 5th Grade) that there are many different types of quadrilaterals and they can be arranged in a hierarchy based on their properties.

Discuss the relationship between the quadrilaterals with your children. Follow the arrows down to see how certain ones are also special types of others as they exhibit all their properties. For example, a square is a special type of rectangle. Indeed a square can be said to be a special case of all the other quadrilaterals shown in the table.

The table shows different types of special quadrilaterals arranged in a hierarchy.

Quadrilateral Properties and Hierarchy

Follow the arrows down (or up if your prefer) the table to view the various categories and sub-categories.

Square

A Square is a quadrilateral with equal-length sides forming four right-angles.

A square is
also a special type
of		 … and it is
also a special type
of
Rhombus Rectangle
A Rhombus is a Quadrilateral in which opposite sides are parallel and all four sides are of equal length. A rectangle is a quadrilateral with four right-angles and opposite sides that are parallel.
A Rhombus is also
a special type
of		 … and it is also a special type
of		 A Rectangle is also
a special type
of
Kite Parallelogram
A Kite is a Quadrilateral in which the sides can be grouped into two pairs of adjacent equal-length sides. A Parallelogram is a quadrilateral in which each of the two pairs of opposite sides are parallel.
A Parallelogram is* also
a special type
of
Trapezoid

A Trapezoid is a Quadrilateral in which two of the sides are parallel.
A Kite is also
a special type
of		 A Trapezoid is also
a special type
of

Quadrilateral

A Quadrilateral is a polygon with four sides.

* Using the Inclusive (not the Exclusive one) definition of a Trapezoid

Worksheets

Click the links below and get your children to try both worksheets.

You can also try a hands-on activity with this worksheet to show that there are 360° in a quadrilateral.