2D shapes
Quadrilaterals
A quadrilateral is any shape with four straight sides. There are seven special quadrilaterals you use a lot: the square, rectangle, parallelogram, trapezium, isosceles trapezium, rhombus and kite. You need to be able to identify, describe and classify them.
What is a quadrilateral?
A quadrilateral is a flat shape with four straight sides. To describe one, we look at its sides (which are equal, which are parallel), its angles, its diagonals and its lines of symmetry. The symbol | (and =) shows sides that are equal. The arrow symbols show sides that are parallel. A small square in a corner shows a 90° angle.
The seven special quadrilaterals
• Square: four equal sides, two pairs of parallel sides, all angles 90°, diagonals bisect each other at 90°, 4 lines of symmetry. • Rectangle: two pairs of equal sides, two pairs of parallel sides, all angles 90°, diagonals bisect each other, 2 lines of symmetry. • Parallelogram: two pairs of equal sides, two pairs of parallel sides, two pairs of equal angles, diagonals bisect each other, 0 lines of symmetry. • Trapezium: one pair of parallel sides. • Isosceles trapezium: one pair of parallel sides, one pair of equal sides, 1 line of symmetry. • Rhombus: four equal sides, two pairs of parallel sides, two pairs of equal angles, diagonals meet at 90°, 2 lines of symmetry. • Kite: two pairs of equal sides, one pair of equal angles, diagonals meet at 90°, 1 line of symmetry, no parallel sides.
Classifying quadrilaterals
To work out which quadrilateral you have, check its properties one by one. For example, if a shape has four equal sides you know it is a square or a rhombus; if its angles are also all 90° it must be a square. The word 'properties' means the same as 'characteristics'.
Worked examples
Describe a rectangle
- A rectangle is a quadrilateral, so it has four sides.
- It has two pairs of equal sides and two pairs of parallel sides.
- The sides meet at 90°, and the diagonals bisect each other.
Answer: A rectangle has two pairs of equal parallel sides, all angles 90°, and 2 lines of symmetry.
Describe a square
- A square is a quadrilateral with four equal sides.
- It has two pairs of parallel sides and every angle is 90°.
- Its diagonals bisect each other at 90°.
Answer: A square has 4 equal sides, all angles 90°, and 4 lines of symmetry.
Describe a parallelogram
- A parallelogram is a quadrilateral with two pairs of equal sides.
- It has two pairs of parallel sides and two pairs of equal angles.
- Its diagonals bisect each other, but it has no lines of symmetry.
Answer: A parallelogram has 2 pairs of parallel sides, 2 pairs of equal angles, and 0 lines of symmetry.
Describe an isosceles trapezium
- A trapezium has one pair of parallel sides.
- An isosceles trapezium also has one pair of equal sides.
- This makes it have one line of symmetry.
Answer: An isosceles trapezium has 1 pair of parallel sides, 1 pair of equal sides, and 1 line of symmetry.
Describe a kite
- A kite is a quadrilateral with two pairs of equal sides that are next to each other.
- It has one pair of equal angles and no parallel sides.
- Its diagonals cross at 90°.
Answer: A kite has 2 pairs of equal sides, diagonals meeting at 90°, and 1 line of symmetry.
Classify from a clue
- A shape is one of the seven special quadrilaterals and has exactly one pair of equal sides.
- A kite has two pairs of equal sides, and a rhombus or square has all four sides equal.
- Only one special quadrilateral has exactly one pair of equal sides.
Answer: The shape must be an isosceles trapezium.
Where you see this in real life
- Square and rectangular tiles fit together with no gaps (they tessellate) on kitchen and bathroom walls.
- A kite you fly in the park is shaped like the kite quadrilateral.
- Windows, doors and picture frames are usually rectangles.
Key words
- Quadrilateral
- A flat shape with four straight sides.
- Parallel
- Two sides that are always the same distance apart and never meet.
- Diagonal
- A straight line joining two opposite corners of a shape.
- Bisect
- To cut something exactly in half.
- Trapezium
- A quadrilateral with one pair of parallel sides (plural: trapezia).