Concept 1 of 6
The Quadrilateral Family: 4-Sided Shapes
Today's big idea
Equal sides and parallel sides together decide which quadrilateral you have.
Square, rectangle, rhombus, parallelogram and trapezium, each with its own rule.
How it works
👀 What's going on?
Any shape with four straight sides is a quadrilateral. That is an enormous family, and its members look nothing like one another. Two questions sort every one of them out.
💡 Here's the trick
Look at the family above. Each member is named by which sides are equal and which sides are parallel. A square has 4 equal sides and 4 right angles. A rhombus keeps the 4 equal sides but drops the right angles. A rectangle keeps the right angles instead. A parallelogram just needs 2 pairs of parallel sides, and a trapezium has exactly 1. A kite has no parallel sides at all, just two pairs of equal sides next to each other.
🪄 How to do it
- 1.Count how many sides are equal, the way the picture above sorts them.
- 2.Count how many corners are right angles.
- 3.Count the pairs of parallel sides, then read off the name.
✍️ Try it
One shape has 4 equal sides and no right angles. Another has exactly one pair of parallel sides. Name each of them.
Four equal sides with no right angles is a rhombus, which is a square pushed over sideways. Exactly one parallel pair is a trapezium. Had it owned two parallel pairs it would be a parallelogram instead.
⚠️ Watch out
You might be thinking a square and a rectangle are two different shapes. A square is a rectangle, because it has 4 right angles, and it is a rhombus too. These names describe rules, and one shape can satisfy several at once.
🌟 Why this matters
Tiles, window frames, kites and road signs are all named this way, and ordering the wrong name gets the wrong shape delivered. Sorting by rule rather than by look is what prevents that.
Exam tip: Questions asking whether a square is a rectangle are testing whether you sort by rule, and the answer is yes.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“A shape has exactly ONE pair of parallel sides. What is it?”
- 1
Count the parallel pairs
Just one pair of sides runs parallel. The other two don't.
- 2
Rule out the others
A parallelogram needs TWO parallel pairs; a square or rhombus need all sides equal too.
- 3
Match the family member
Exactly one parallel pair = trapezium.
- 4
Answer ✓
It's a trapezium
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Count the sides: 3 = triangle, 4 = quadrilateral, 5+ = other polygon.
SHAPE SORT · ROUND 1 OF 2 · SORT ALL 6
Quick check
✅ VERIFICATION
Which statement is true?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Sorting Triangles by Sides
Equilateral, isosceles or scalene?