Special quadrilaterals — properties

A quadrilateral is any 4-sided polygon. WJEC tests recognition + properties heavily on Foundation, and uses the properties as bricks for proof at Higher.

Square

• All 4 sides equal.
• All 4 angles 90°.
• Diagonals: equal length, bisect each other at right angles, bisect interior angles.
• 4 lines of symmetry, rotational symmetry order 4.

Rectangle

• Opposite sides equal and parallel.
• All 4 angles 90°.
• Diagonals: equal length, bisect each other (but NOT at right angles, unless square).
• 2 lines of symmetry, rotational symmetry order 2.

Rhombus

• All 4 sides equal.
• Opposite angles equal; opposite sides parallel.
• Diagonals: bisect each other at right angles, bisect interior angles. NOT necessarily equal.
• 2 lines of symmetry (along diagonals), rotational symmetry order 2.

Parallelogram

• Opposite sides equal and parallel.
• Opposite angles equal; co-interior angles supplementary (sum to 180°).
• Diagonals bisect each other (but not at right angles, not equal — unless rectangle/rhombus).
• No lines of symmetry, rotational symmetry order 2.

Trapezium

• One pair of parallel sides (called the bases).
• An isosceles trapezium has equal non-parallel sides; one line of symmetry.

Kite

• Two pairs of adjacent sides equal.
• One pair of opposite angles equal (between the unequal sides).
• One diagonal bisects the other at right angles.
• 1 line of symmetry, no rotational symmetry.

Angle sum

Every quadrilateral has interior angles summing to 360°. Always.

WJEC exam tip

WJEC frequently asks "name the quadrilateral with these properties: ...". List the properties in your head and pick the most specific match. A square is also a rectangle, but if all sides equal, square is the better answer.