Properties of quadrilaterals

Quadrilaterals have four sides and their angles add to 360°. Each special quadrilateral has its own properties: equal sides, parallel sides, right angles and how its diagonals behave.

Key facts

  • Square: 4 equal sides, 4 right angles.
  • Rectangle: opposite sides equal, 4 right angles.
  • Rhombus: 4 equal sides, opposite angles equal.
  • Parallelogram: opposite sides parallel and equal.
  • Trapezium: one pair of parallel sides. Kite: two pairs of equal adjacent sides.
  • Angles in a quadrilateral add to 360°.

Worked examples

Example 1

Three angles of a quadrilateral are 85°, 95° and 110°. Find the fourth.

  1. 85 + 95 + 110 = 290
  2. 360 − 290 = 70°

Answer: 70°

Example 2

Which quadrilaterals have diagonals that cross at right angles?

  1. In a square, rhombus and kite the diagonals are perpendicular.
  2. In a rectangle and a general parallelogram they are not.

Answer: Square, rhombus and kite