6.2 Quadrilaterals

Quadrilaterals

A quadrilateral is any polygon with four sides. The basic quadrilaterals are the trapezium, parallelogram, rectangle, rhombus, square and kite.

Trapezium

A trapezium is a quadrilateral with one pair of parallel opposite sides. It may also be called a trapezoid . A special type of trapezium is the isosceles trapezium , where one pair of opposite sides is parallel, the other pair of sides is equal in length and the angles at the ends of each parallel side are equal. An isosceles trapezium has one line of symmetry and its diagonals are equal in length.

Parallelogram

A trapezium with both sets of opposite sides parallel is called a parallelogram . A summary of the properties of a parallelogram is:

• Both pairs of opposite sides are parallel.
• Both pairs of opposite sides are equal in length.
• Both pairs of opposite angles are equal.
• Both diagonals bisect each other (i.e. they cut each other in half).

Rectangle

A rectangle is a parallelogram that has all four angles equal to ${90}^{\circ }$ . A summary of the properties of a rectangle is:

• Both pairs of opposite sides are parallel.
• Both pairs of opposite sides are of equal length.
• Both diagonals bisect each other.
• Diagonals are equal in length.
• All angles at the corners are right angles.

Rhombus

A rhombus is a parallelogram that has all four sides of equal length. A summary of the properties of a rhombus is:

• Both pairs of opposite sides are parallel.
• All sides are equal in length.
• Both pairs of opposite angles are equal.
• Both diagonals bisect each other at ${90}^{\circ }$ .
• Diagonals of a rhombus bisect both pairs of opposite angles.

Square

A square is a rhombus that has all four angles equal to 90 ${}^{\circ }$ .

A summary of the properties of a square is:

• Both pairs of opposite sides are parallel.
• All sides are equal in length.
• All angles are equal to ${90}^{\circ }$ .
• Both pairs of opposite angles are equal.
• Both diagonals bisect each other at ${90}^{\circ }$ .
• Diagonals are equal in length.
• Diagonals bisect both pairs of opposite angles (ie. all ${45}^{\circ }$ ).

Kite

A kite is a quadrilateral with two pairs of adjacent sides equal.

A summary of the properties of a kite is:

• Two pairs of adjacent sides are equal in length.
• One pair of opposite angles are equal where the angles are between unequal sides.
• One diagonal bisects the other diagonal and one diagonal bisects one pair of opposite angles.
• Diagonals intersect at right-angles.