Classifying quadrilaterals

Quadrilaterals are sorted by the properties of their sides and angles. They form a hierarchy.

Hierarchy

quadrilateral
  ├── trapezoid    (1 pair of parallel sides)
  └── parallelogram  (2 pairs of parallel sides)
        ├── rhombus     (all sides equal)
        ├── rectangle   (4 right angles)
        └── square      (all sides equal + 4 right angles)

Key features

• Trapezoid: one pair of parallel sides.
• Parallelogram: two pairs of parallel sides. Opposite sides are equal.
• Rhombus: a parallelogram with all sides equal.
• Rectangle: a parallelogram with 4 right angles.
• Square: both a rectangle and a rhombus at once — all sides equal and 4 right angles.

Quick decision grid

Common traps

• A square is a special rectangle and also a special rhombus. This means every square is a rectangle, but not every rectangle is a square.
• A parallelogram is not a trapezoid in the traditional classification used here (a trapezoid has only one pair of parallel sides).
• A rhombus with right angles is in fact a square.

Try it yourself

• Classifying quadrilaterals
• Area of a parallelogram