Classifying quadrilaterals
A quadrilateral is any closed shape with four straight sides. Open a maths book and you will see at least five different kinds with their own names. Their differences come from three questions:
- How many pairs of parallel sides are there?
- Are any sides the same length?
- Are any angles right angles?
The family of quadrilaterals
| Name | Parallel pairs | Equal sides | Right angles |
|---|---|---|---|
| trapezium | exactly 1 pair | not required | not required |
| parallelogram | 2 pairs (opposite sides) | opposite sides equal | not required |
| rhombus | 2 pairs | all four sides equal | not required |
| rectangle | 2 pairs | opposite sides equal | all four are right angles |
| square | 2 pairs | all four sides equal | all four are right angles |
A square is a special rectangle (it has the extra "all sides equal" feature). A square is also a special rhombus (it has the extra "right angles" feature).
How to tell them apart in a picture
- Look first at the parallel marks (the arrows on the sides). One pair → trapezium. Two pairs → parallelogram, rhombus, rectangle or square.
- If there are two pairs of parallel sides and all sides have the same tick marks → rhombus (or square if it also has right angles).
- If there are two pairs of parallel sides and all four corners are right angles → rectangle (or square if all sides are equal too).
- If you see only one pair of parallel sides → trapezium.
What about a kite?
A kite has two pairs of equal sides, but they sit next to each other (not opposite). A kite is not a parallelogram. In some countries Year-4 also meets the kite by name; in others it appears later.
A worked example
A four-sided shape has all sides 4 cm long. Two of its angles are 70° and two are 110°. Name it.
- All sides equal → rhombus (could be a square too, but only if angles are 90°, which they are not).
- No right angles → not a square.
Answer: a rhombus.
Another shape has sides 5 cm, 8 cm, 5 cm, 8 cm. Two pairs of parallel sides and four right angles. Name it.
- Opposite sides equal, four right angles, two pairs parallel → rectangle (not a square, because not all sides equal).
Why these names matter
When you build something — a picture frame, a tile pattern, a robot — you choose shapes by their properties, not by how they look at first glance. "Rectangle" tells the builder: opposite sides equal, four right angles. That's enough to cut the wood. The names are a shorthand for a list of rules.
What's next
- Parallel and perpendicular lines — the test for "two pairs of parallel sides"
- Classifying triangles
- Back to the introduction