Properties of Quadrilaterals - square, rectangle, rhombus, parallelogram, kite, trapezoid

Author:: Mark

A quadrilateral is the name given to any shape with 4 sides. All the angles in a quadrilateral will sum to 360⁰. In this hub we will take a look at the main quadrilaterals that come up in math tests and list their main mathematical properties:

A square has 4 equal side lengths and contains four right angles. It has 4 lines of reflectional symmetry and also has order 4 rotational symmetry.

A rectangle (or oblong) has 2 pairs of equal side lengths and like a square contains 4 right angles. It has 2 lines of reflectional symmetry and has order 2 rotational symmetry.

A rhombus (looks like a diamond) has 4 equal side lengths and also has 2 pairs of parallel sides. The angles opposite each other are equal in size. It also has 2 lines of reflectional symmetry and has order 2 rotational symmetry.

A parallelogram looks a bit like a “squashed rectangle”. Just like a rectangle is has 2 pairs of equal side lengths and also has 2 pairs of parallel sides. Also the angles opposite each other are the same size. A parallelogram doesn’t have reflectional symmetry and the order of rotational symmetry is order 2. Make sure you remember these facts as parallelograms are quite a popular question on math tests as many students assume that a parallelogram has 2 lines of reflectional symmetry.

Probably one of the easiest quadrilaterals to recognise is a kite. A kite has 2 pairs of equal sides and 1 pair of equal angles. It also has 1 line of reflectional symmetry but it doesn’t have rotational symmetry (order 1). If you draw in all of the diagonals of a kite they will meet at right angles in the centre of the kite.

A trapezium or trapezoid is one of the trickiest shapes to get right in math tests as it can be drawn in different ways. The main property of a trapezoid is that it has one pair of parallel sides.