Quadrilaterals belong to families, and one shape can belong to several. A rectangle is any quadrilateral with 4 right angles, so every square is a rectangle. A rhombus is any quadrilateral with 4 equal sides, so every square is a rhombus too. Rectangles and rhombuses are both parallelograms. To test 'Is every A a B?', write down what a B needs, then ask whether every A always has it. Careful: the reverse is often false. Every square is a rectangle, but a long thin rectangle is not a square. Some facts force others: a parallelogram with one right angle has four.
Explore this idea with maths tools
Maths you can move
Build 8 + 5
Tap two gold counters to fill the ten-frame.
8 in the frame + 5 waiting. The total stays the same.
Words to know
- definition
- the facts a shape must have to get its name
- every
- all of them, with no exceptions
Worked examples
Is every square a rectangle?
- 1.A rectangle needs 4 right angles.
- 2.Every square has 4 right angles.
= yes
Is every parallelogram a rhombus?
- 1.A rhombus needs 4 equal sides.
- 2.A parallelogram can have 2 long and 2 short sides.
= no
A parallelogram has one right angle. Must it be a rectangle?
- 1.Angles next to each other in a parallelogram add to 180°, so the next angle is 90° too.
- 2.All 4 angles are right angles.
= yes
For parents
Method: List what the second shape needs and check the first shape always has it.
What to say: What does a rectangle need? Does every square have that? Can you draw one that doesn't?
Common mistakes:
- Treats each quadrilateral name as a separate box, so denies that a square is a rectangle or a rhombus is a parallelogram.
- Assumes a statement works backwards: because every square is a rectangle, thinks every rectangle is a square.
- Decides two shapes belong together because they share one property (both have parallel sides), without checking the rest.
- Will not conclude a shape is special unless every property is stated, missing facts that are forced (a parallelogram with one right angle has four).
- Thinks one property is enough to name a special shape (four equal sides must mean a square).