Topics · Primary Maths · Quadrilaterals
Quadrilaterals: one family, five names
Any closed shape with four straight sides. The five that get names are all the same shape with conditions added — which sides are parallel, which are equal, which angles are right — and the names are what those conditions are for.
- 479 exam papers analysed
- appears in 99% of P6 Maths papers
- ~4 min read
01 Start here
A quadrilateral is any closed shape with four straight sides. That is the whole definition — the sides can be any lengths and point any way.
It comes with one fact that never moves: the four angles always total 360°. However lopsided the shape, that total holds.
Every other shape on this page is a quadrilateral with a condition added. Nothing here is a separate kind of shape.
Shapes with three sides are the other family, and they have their own page: triangles, where the angles total 180° instead.
02 The family
Read it downwards: each shape is also every shape it hangs from. A square sits at the bottom, so a square is a rhombus and a rectangle and a parallelogram and a quadrilateral, all at the same time.
That is the part most often got wrong, and it is why a list of five separate definitions does not work. These are not five different shapes standing side by side. They are one shape with conditions added.
03 How to tell them apart
Work down the questions in order and stop when the answer is no. The marks on the diagrams are how a paper tells you the answer without saying it.
- Count the pairs of parallel sides. None, and it is just a quadrilateral. One pair → trapezium, and you are done. Two pairs → parallelogram, keep going.
- Are all four sides equal? Yes → it is a rhombus.
- Are all four angles right angles? Yes → it is a rectangle.
- Both? → it is a square — and it is still a rhombus and still a rectangle.
04 How to say them
These are words most children have never said out loud, and a word you cannot say is a word you avoid using. Capitals mark the syllable you lean on. Tap the speaker to hear it.
- quadrilateralsaykwod-ri-LAT-uh-ruhlmore than onequadrilaterals
Any closed shape with four straight sides. Every other word here is one of these.
- angle ABC, written ∠ABCsayANG-guhl A B C
The angle at B, the middle letter. The outer letters say which two sides form it, so ∠ABC is the corner where BA meets BC. Papers name angles this way because once a shape is cut in two, a bare “angle B” no longer says which of the pieces is meant.
- parallelsayPA-ruh-lel
Two lines that run in the same direction and never meet, however far you extend them. Marked with matching arrows.
- trapeziumsaytruh-PEE-zee-ummore than onetrapeziums, or trapezia
A quadrilateral with exactly one pair of parallel sides. American books call this a trapezoid; Singapore papers say trapezium.
- parallelogramsaypa-ruh-LEL-uh-grammore than oneparallelograms
A quadrilateral with two pairs of parallel sides. Opposite sides are equal.
- rhombussayROM-bussmore than onerhombuses, or rhombi
A parallelogram with all four sides equal. Often drawn balanced on a corner, which is why it gets called a diamond.
- rectanglesayREK-tang-guhlmore than onerectangles
A parallelogram with four right angles.
- squaresayskwairmore than onesquares
Four equal sides and four right angles. That makes it a rhombus and a rectangle at the same time.
- perpendicularsaypur-pen-DIK-yuh-luh
Two lines that meet at a right angle, 90°. Marked with a small square in the corner.
05 What each level is tested on
The same topic, asked differently as it goes up. The percentage is the share of papers at that level in which it appears.
- P2
Naming squares and rectangles on sight, and counting sides and corners.
Practise P2 Quadrilaterals — 10 questions →59% of P2 papers
- P3
Sorting four-sided shapes by their properties, and the first parallel and perpendicular sides.
Practise P3 Quadrilaterals — 10 questions →50% of P3 papers
- P4
Properties in earnest: which shape has equal sides, which has right angles, and telling squares, rectangles and rhombuses apart.
Practise P4 Quadrilaterals — 10 questions →85% of P4 papers
- P5
Angles inside the shape, and finding an unknown one using what the shape guarantees.
Practise P5 Quadrilaterals — 10 questions →82% of P5 papers
- P6
Angle sums and composite figures, where a shape is cut into or built out of these five.
Practise P6 Quadrilaterals — 10 questions →99% of P6 papers
06 Mistakes worth knowing about
Each of these is wrong. Decide why before you open it.
“A rhombus has no right angles.”
A rhombus with right angles is a square, and a square is still a rhombus. What makes a shape a rhombus is four equal sides — the angles are not part of it.
“A square is not a rectangle.”
It is one. A rectangle needs four right angles, and a square has four right angles. Having equal sides as well does not stop it being a rectangle.
“A trapezium has two pairs of parallel sides.”
One pair. As soon as the second pair is parallel the shape is a parallelogram.
“Opposite sides of a parallelogram are equal, so all four sides are equal.”
Equal in opposite pairs only. All four equal is the extra condition that turns a parallelogram into a rhombus.
“A rhombus is a diamond, so it is a different shape when you turn it.”
Turning a shape never changes what it is. A square balanced on one corner is still a square, not a rhombus that stopped being a square.
Now try it
50 questions across 5 levels, marked as you go with the working shown.