Types of Quadrilaterals- Complete Classification

What Is a Quadrilateral?

A quadrilateral is a four-sided polygon. That's the whole definition. Four sides, four angles, and that's it. The sum of its interior angles is always 360° — no exceptions, no tricks.

Most people think "square" when they hear quadrilateral. That's wrong. There's a whole family of these shapes, and they get confusing fast. This guide cuts through the noise.

The Quadrilateral Family Tree

Not all quadrilaterals are equal. They stack into a hierarchy based on their properties. Here's how it breaks down:

Everything else — squares, rectangles, rhombuses, parallelograms — is a special type of trapezoid. Mathematicians argue about this, but in most geometry contexts, that's how it works.

The Main Types of Quadrilaterals

1. Square

The square is the perfectionist of the quadrilateral world. It has:

A square is simultaneously a rectangle, a rhombus, and a parallelogram. It's the overachiever. If a shape can have a property, a square probably has it.

2. Rectangle

Rectangles have opposite sides that are equal and parallel. That's the key difference from a square — not all sides are equal. You get:

Every square is a rectangle. Not every rectangle is a square. Keep that straight.

3. Rhombus

Think of a rhombus as a "pushed over" square. All four sides are equal, but the angles aren't 90°. You get:

Think of a diamond shape. That's a rhombus. A square is just a rhombus with right angles.

4. Parallelogram

This is where things get looser. A parallelogram has:

Rectangles, rhombuses, and squares are all parallelograms. A parallelogram is the most basic shape in this family — it has just enough properties to be useful without being special.

5. Trapezoid (US) / Trapezium (UK)

Here's where geography matters. In the US, a trapezoid has one pair of parallel sides. In the UK, that's a trapezium. Confusing? Yes. Just deal with it.

6. Isosceles Trapezoid

A trapezoid with a twist — the non-parallel sides are equal. This gives you:

7. Kite

A kite has two pairs of adjacent sides that are equal. The pairs don't share sides — they meet at different vertices. You get:

Think of a kite flying in the air. That's the shape.

8. General Quadrilateral

This is the leftovers category. A general quadrilateral has no parallel sides, no equal sides, and no special properties. It's just four connected line segments. You can only say for certain that its angles sum to 360°.

Properties Comparison Table

Shape Sides Angles Diagonals
Square 4 equal 4 right angles Perpendicular, equal
Rectangle Opposite equal 4 right angles Equal, bisect each other
Rhombus 4 equal Opposite equal Perpendicular
Parallelogram Opposite equal Opposite equal Bisect each other
Trapezoid None equal required No requirements No special properties
Kite Adjacent pairs equal One pair equal Perpendicular

How to Identify Which Quadrilateral You Have

Stop guessing. Use this step-by-step approach:

  1. Count the sides. If it's not four, it's not a quadrilateral.
  2. Check for parallel sides. Two pairs means parallelogram family. One pair means trapezoid.
  3. Check side lengths. All equal → square or rhombus. Opposite equal → rectangle or parallelogram. Adjacent equal → kite.
  4. Check angles. All 90° → rectangle or square. Not 90° → rhombus or general parallelogram.
  5. Check diagonals. Equal diagonals → rectangle or isosceles trapezoid. Perpendicular → square, rhombus, or kite. Bisect each other → parallelogram family.

Common Mistakes

Quick Reference Cheat Sheet

That's the complete classification. Memorize the properties, and you can identify any quadrilateral in seconds.