Quadrilaterals

A quadrilateral is a 2D shape with four sides.

There are six special quadrilaterals with different properties.

Square

Lines that come from each corner of a square, form a right angle at the centre
  • A square has four sides of equal length.
  • It has four right angles (90°).
  • The opposite sides are parallel.
  • The diagonals bisect each other at right angles.

Rectangle

Lines that come from each corner of a square, meet at a point in the centre
  • A rectangle has two pairs of equal sides.
  • It has four right angles (90°).
  • The opposite sides are parallel.
  • The diagonals bisect each other.

Parallelogram

Lines that come from each corner of a parallelogram, meet at a point in the centre
  • A parallelogram has two pairs of equal sides.
  • It has two pairs of equal angles.
  • The opposite sides are parallel.
  • The diagonals bisect each other.

Rhombus

Lines that come from each corner of a parallelogram, form a right angle at the centre
  • A rhombus has four sides of equal lengths.
  • It has two pairs of equal angles.
  • The opposite sides are parallel.
  • The diagonals bisect each other at right angles.

Trapezium

Trapezium
  • A trapezium has one pair of parallel sides.

Kite

Kite shape, where the intersecting lines from each corner, produce a right angle at the centre
  • A kite has two pairs of equal sides.
  • It has one pair of equal angles.
  • The diagonals bisect at right angles.

The sum of interior angles in a quadrilateral

curriculum-key-fact
The sum of interior angles in a quadrilateral is 360°.

This fact and the properties of quadrilaterals can be used to calculate angles.

Example

Find angle d.

Quadrilateral shape with angles, 100degrees, 70degrees, 30degrees & unknown angle d

d = 360 - 100 - 70 - 30 = 160^\circ

Question

Find the unknown angles.

Parallelogram with angles of 50 degrees and unknown angles, f & g

The quadrilateral is a parallelogram. Opposite angles are equal.

g = 50^\circ

Angles in a quadrilateral add up to 360° and opposite angles are equal.

f = \frac{360 - 50 - 50}{2} = 130^\circ