Properties of quadrilaterals · Year 7

In Year 7 you learn: diagonals and properties.

A quadrilateral is any four-sided shape. Squares, rectangles, rhombuses, parallelograms, trapeziums and kites each have their own properties of sides, angles, diagonals and symmetry, which help us name them and find missing angles.

Key facts

  • The angles in any quadrilateral add up to 360°.
  • Parallelogram: opposite sides equal and parallel; opposite angles equal; neighbouring angles add to 180°.
  • Rhombus: a parallelogram with four equal sides; diagonals cross at right angles.
  • Rectangle: four right angles; diagonals equal. A square is both a rectangle and a rhombus.
  • Trapezium: exactly one pair of parallel sides. Kite: two pairs of equal adjacent sides, one pair of equal opposite angles.

Worked examples

Example 1

Three angles of a quadrilateral are 85°, 110° and 72°. Find the fourth angle x.

Answer: x = 93°

Example 2

ABCD is a parallelogram with angle A = 64°. Find angles B, C and D.

Answer: B = 116°, C = 64°, D = 116°

Example 3

The angles of a quadrilateral are x, 2x, 3x and 4x. Find the largest angle.

Answer: 144°

Other years