Quadrilaterals
A polygon is a flat‑surfaced shape. A quadrilateral is a four‑sided polygon.
Rectangle
A rectangle is a quadrilateral whose opposite sides are equal and parallel.
All the angles of a rectangle are right angles.
AB = DC and AD = BC
It has rotational symmetry of order 2 (½‑turn symmetry).
The diagonals of a rectangle are equal and bisect each other.
AC = BD and OA = OB = OC = OD
Square
A square is a special rectangle. It is a rectangle with all its sides equal.
AB ∥ CD and AD ∥ BC
AB = BC = CD = DA
It has rotational symmetry of order 4 (¼‑turn symmetry).
The diagonals of a square:
- bisect the angles of the square
- bisect each other at right angles
- bisect the corner angles
Kite
It has no rotational symmetry.
A kite has two pairs of adjacent sides equal.
An inverted kite
The diagonals cross at right angles, but do not bisect each other.
Rhombus
It has rotational symmetry of order 2 (½‑turn symmetry).
The diagonals of a rhombus bisect each other at right angles and bisect the corner angles.
The opposite sides of a rhombus are parallel.
All sides are equal, and opposite angles are equal.
Parallelogram
It has rotational symmetry of order 2 (½‑turn symmetry).
The opposite sides of a parallelogram are equal and parallel.
The opposite angles are equal.
Trapezium
It has no rotational symmetry.
An ordinary trapezium has no axis of symmetry.
An isosceles trapezium has one axis of symmetry.
Ordinary trapezium
Isosceles trapezium
