X Tables
geometry

Properties of quadrilaterals

Explore squares, rectangles, rhombuses, parallelograms, kites and trapezia.

Quick answer

A quadrilateral is any shape with four straight sides and four corners. Different quadrilaterals have different properties, like how many equal sides they have, what their angles look like, and whether their sides are parallel.

Learning outcome

By the end of this page, you will be able to identify and describe the properties of different types of quadrilaterals – squares, rectangles, rhombuses, parallelograms, kites, and trapezia – and explain how they are alike and different. Success signs:
  • You can name at least 3 different types of quadrilaterals
  • You can tell the difference between a square and a rectangle
  • You can explain how many sides and corners a quadrilateral has
  • You can draw or show a quadrilateral with special features

Why this matters

Understanding the properties of quadrilaterals helps you see maths all around you. You use this knowledge when you look at the shape of your bedroom, build with blocks, play football on a rectangular pitch, or even when you're drawing a picture. Knowing these shapes helps you understand how things fit together, how they look, and how to describe them clearly. This is important for more advanced maths in school and for real-life problem solving.

How it works

A quadrilateral is any shape that has exactly four straight sides and four corners (also called vertices). The word comes from "quad" meaning four and "lateral" meaning sides. Each shape has special features that make it unique. Let’s look at the most common quadrilaterals:
  • Square: Four equal sides and four right angles (90°)
  • Rectangle: Four sides with opposite sides equal and four right angles
  • Rhombus: Four equal sides, but angles are not right angles
  • Parallelogram: Opposite sides are equal and parallel
  • Kite: Two pairs of adjacent equal sides
  • Trapezium: At least one pair of parallel sides

Examples you can see

Let’s imagine you’re looking at a playground. You see a shape drawn in chalk on the ground. What could it be? Example 1: Square A square has four equal sides and four right angles. If you look at a tile on the floor, it might look like this:
  • Each side is the same length
  • Each corner is a perfect L-shape (90°)
Example 2: Rectangle A rectangle has opposite sides equal and four right angles. A book or a window is a rectangle:
  • Two sides are longer, two are shorter
  • All corners are right angles
Example 3: Rhombus A rhombus looks like a diamond. It has four equal sides but not all angles are right angles:
  • All sides are the same length
  • Opposite angles are equal
Example 4: Parallelogram A parallelogram has opposite sides that are equal and parallel:
  • It looks like a slanted rectangle
  • Opposite sides are the same length and run in the same direction
Example 5: Kite A kite looks like the ones you fly in the sky, but it can also be drawn on paper:
  • Two pairs of adjacent sides are equal
  • One pair of opposite angles are equal
Example 6: Trapezium A trapezium has at least one pair of parallel sides:
  • It can look like a house with a flat roof
  • It might have one pair of sides that never meet

Try it as a mini adventure

Adventure: Shape Hunt in Your Home You are a shape detective! Your mission is to find and describe different quadrilaterals in your home. Step 1: Look around your living room and find a square (like a picture frame or a tile on the floor). How many equal sides does it have? Step 2: Find a rectangle (like a book or a door). Are the opposite sides the same length? Step 3: Look for a rhombus (like a diamond-shaped window or a kite). Do all the sides look the same? Step 4: Find a parallelogram (like a slanted bookshelf or a window that’s been pushed). Are opposite sides the same and running in the same direction? Step 5: Find a kite shape (like a kite or a diamond-shaped toy). Do two pairs of sides next to each other match? Step 6: Look for a trapezium (like a roof or a table with one pair of parallel sides). Can you see two sides that are parallel? Step 7: Draw or write about each shape you found. Describe its special features!

Common mistakes

  • Mistake: Thinking a rectangle and a square are the same. Why it happens: Both have four right angles and four sides, but a square has all sides equal. Fix: Remember that a square has four equal sides, while a rectangle has opposite sides equal.
  • Mistake: Confusing a rhombus with a square. Why it happens: Both have four equal sides, but a rhombus does not have right angles. Fix: A rhombus has equal sides but can be slanted, while a square has equal sides and right angles.
  • Mistake: Thinking that all quadrilaterals must have equal sides. Why it happens: Some shapes are more obvious than others. Fix: A quadrilateral just needs four straight sides and four corners – it doesn’t need to have equal sides.
  • Mistake: Calling a kite a rhombus. Why it happens: Both have equal sides, but the arrangement is different. Fix: A kite has two pairs of adjacent equal sides, not opposite sides.

Parent and carer guide

As a parent or carer, you can help your child understand quadrilaterals by:
  • Looking around your home together and identifying shapes
  • Using real objects like books, tiles, or windows to show different shapes
  • Encouraging your child to describe what they see
  • Playing shape games like "I spy with my little eye a shape with four sides"
  • Using drawing or cutting shapes to make it hands-on
  • Reinforcing that it's okay to make mistakes – they help us learn
If your child gets confused, remember that it’s normal to mix up shapes at first. Keep the learning fun and keep asking questions like:
  • How many sides does this shape have?
  • Are the sides the same length?
  • Do the corners look like right angles?

Practice questions

  1. How many sides does a quadrilateral have?
  2. Which shape has four equal sides and four right angles?
  3. Which shape has opposite sides equal and parallel?
  4. Which shape has two pairs of adjacent equal sides?
  5. Which shape has at least one pair of parallel sides?
Answers:
  1. Four
  2. Square
  3. Parallelogram
  4. Kite
  5. Trapezium

FAQ

What is a quadrilateral?

A quadrilateral is any shape with four straight sides and four corners.

Are all squares rectangles?

Yes, all squares are rectangles because they have four right angles and four sides. But not all rectangles are squares.

Can a quadrilateral have no equal sides?

Yes, a quadrilateral can have no equal sides. For example, a trapezium can have four sides of different lengths.

What’s the difference between a rhombus and a square?

A rhombus has four equal sides but not all angles are right angles, while a square has four equal sides and four right angles.

Can a parallelogram be a rectangle?

Yes, a rectangle is a special type of parallelogram where all angles are right angles.