Quadrilaterals: Types and properties

In a nutshell

Quadrilaterals are four-sided shapes, with four corners and four sides. Angles in a quadrilateral add up to $360\degree$ . There are many different kinds of quadrilaterals.

Properties of quadrilaterals

NAME	PROPERTIES	DIAGRAM
Square	The only regular quadrilateral. Four sides of equal length. Four right angles. The diagonals bisect at right angles. The diagonals are of equal lengths. Two pairs of parallel sides.
Rectangle	Two pairs of equal sides. Four right angles. Two pairs of parallel sides. The diagonals bisect each other.
Rhombus	All four sides are of equal length. Opposite sides are parallel. Opposite angles are equal. The diagonals bisect at right angles. A type of parallelogram.
Parallelogram	Opposite sides are the same length. Opposite sides are parallel. Opposite angles are equal. Diagonals bisect.
Trapezium	Only one pair of parallel sides.
Kite	Two pairs of equal sides adjacent to each other. One pair of opposite angles are equal. No sides are parallel. Diagonals cross at right angles. One line of symmetry.
Arrowhead	Two sets of adjacent sides are equal. One interior angle is a reflex angle. Two interior angles adjacent to the reflex angle are equal. Contains one line of symmetry.

Example 1

Can you identify this quadrilateral from its properties?

Properties include:

It has four sides of an equal length.
Opposite sides are parallel.
Opposite angles are equal.
Its diagonals bisect at right angles.
Has no interior right angles.

First it can help to sketch the shape to identify it.

Maths; Shapes; KS3 Year 7; Quadrilaterals: Types and properties

Therefore, this quadrilateral is a rhombus.

Example 2

Can you identify this quadrilateral from its properties?

Properties include:

Two pairs of equal sides adjacent to each other.
One pair of opposite angles are equal.
No sides are parallel.
Diagonals cross at right angles.
It has one line of symmetry.

First it can help to sketch the shape to identify it.

Maths; Shapes; KS3 Year 7; Quadrilaterals: Types and properties

Therefore, this quadrilateral is a kite.